We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

We present a new formulation to construct numerically equilibrium
configurations of rotating stars in general relativity. Having in mind the
application to their quasi static evolutions, we adopt a Lagrangian formulation
of our own devising, in which we solve force balance equations to seek for the
positions of fluid elements assigned to the grid points, instead of the
ordinary Eulerian formulation. Unlike previous works in the literature, we do
not employ the first integral of the Euler equation, which is not obtained by
an analytic integration in general. We assign a mass, specific angular momentum
and entropy to each fluid element in contrast to the previous methods, in which
the spatial distribution of the angular velocity or angular momentum is
specified. Those distributions are determined after the positions of all fluid
elements (or grid points) are derived in our formulation. We solve the large
system of algebraic nonlinear equations that are obtained by discretizing the
time-independent Euler and Einstein equations in the finite-elements method by
using our new multi-dimensional root-finding scheme, named the W4 method. To
demonstrate the capability of our new formulation, we construct some rotational
configurations both barotropic and baroclinic. We also solve three evolutionary
sequences that mimic the cooling, mass-loss, and mass-accretion as simple toy
models.

We proposed in this paper a new method, which we named the W4 method, to
solve nonlinear equation systems. It may be regarded as an extension of the
Newton-Raphson~(NR) method to be used when the method fails. Indeed our method
can be applied not only to ordinary problems with non-singular Jacobian
matrices but also to problems with singular Jacobians, which essentially all
previous methods that employ the inversion of the Jacobian matrix have failed
to solve. In this article, we demonstrate that (i) our new scheme can define a
non-singular iteration map even for those problems by utilizing the singular
value decomposition, (ii) a series of vectors in the new iteration map
converges to the right solution under a certain condition, (iii) the standard
two-dimensional problems in the literature that no single method proposed so
far has been able to solve completely are all solved by our new method.

Black holes are thought to describe the geometry of massive, dark compact objects in the Universe. To further support and quantify this long-held belief requires knowledge of possible, if exotic alternatives. Here, we wish to understand how compact can self-gravitating solutions be. We discuss theories with a well-posed initial value problem, consisting in either a single self-interacting scalar, vector or both. We focus on spherically symmetric solutions, investigating the influence of self-interacting potentials into the compactness of the solutions, in particular those that allow for flat-spacetime solutions. We are able to connect such stars to hairy black hole solutions, which emerge as a zero-mass black hole. We show that such stars can have light rings, but their compactness is never parametrically close to that of black holes. The challenge of finding black hole mimickers to investigate full numerical-relativity binary setups remains open.

We numerically study the primordial black hole (PBH) formation by an
isocurvature perturbation of a massless scalar field on super Hubble scales in
the radiation-dominated universe. As a first step we perform simulations of
spherically symmetric configurations. For the initial condition, we employ the
spatial gradient expansion and provide the general form of the growing mode
solutions valid up through the second order in this expansion. The initial
scalar field profile is assumed to be Gaussian with a characteristic comoving
wavenumber $k$; $\sim\exp(-k^2R^2)$, where $R$ is the radial coordinate. We
find that a PBH is formed for a sufficiently large amplitude of the scalar
field profile. Nevertheless, we find that the late time behavior of the
gravitational collapse is dominated by the dynamics of the fluid but not by the
scalar field, which is analogous to the PBH formation from an adiabatic
perturbation in the radiation-dominated universe.

Using full Boltzmann neutrino transport, we performed two-dimensional (2D)
core-collapse supernova simulations in axisymmetry for two progenitor models
with 11.2M and 15.0M both rotational and non-rotational. We employed the
results obtained in the early post-bounce phase (t < 20 ms) to assess
performance under rapid rotation of some closure relations commonly employed in
the truncated moment method. We first made a comparison in 1D under spherical
symmetry, though, of the Eddington factor p defined in the fluid rest frame
(FR). We confirmed that the maximum entropy closure for the Fermionic
distribution (MEFD) performs better than others near the proto-neutron star
surface, where p < 1/3 occurs, but does not work well even in 1D when the phase
space occupancy satisfies e < 0.5 together with p < 1/3, the condition known to
be not represented by MEFD. For the 2D models with the rapid rotation, we
employed the principal-axis analysis of the Eddington tensor. We paid
particular attention to the direction of the longest principal axis. We
observed in FR that it is aligned neither with the radial direction nor with
the neutrino flux in 2D, particularly so in convective and/or rapidly rotating
regions, the fact not accommodated in the moment method. We repeated the same
analysis in the laboratory frame (LB) and found again that the direction of the
longest principal axis is not well reproduced by MEFD because the interpolation
between the optically thick and thin limits is not very accurate in this frame.

We develop a neutrino transfer code for core-collapse simulations that directly solves the multidimensional Boltzmann equations in full general relativity. We employ the discrete ordinate method, which discretizes the 6D phase space. The code is an extension of our special relativistic code coupled to a Newtonian hydrodynamics code, which is currently employed for core-collapse supernova simulations. In order to demonstrate our code's capability to treat general relativistic effects, we conduct some tests. We first compute the free streaming of neutrinos in the Schwarzschild and Kerr spacetimes and compare the results with the geodesic curves; in the Schwarzschild case, we deploy not only a 1D grid in space under spherical symmetry but also a 2D spatial mesh under axisymmetry in order to assess the capability of the code to compute the spatial advection of neutrinos. Second, we calculate the neutrino transport in a fixed matter background, which is taken from a core-collapse supernova simulation with our general relativistic but spherically symmetric Boltzmann hydrodynamics code, to obtain a steady neutrino distribution; the results are compared with those given by the latter code.

We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post-Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai-Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.

We report on the core-collapse supernova simulation we conducted for a 11.2M⊙ progenitor model in threedimensional space up to 20 ms after bounce, using a radiation-hydrodynamics code with full Boltzmann neutrino transport. We solve the six-dimensional Boltzmann equations for three neutrino species and the three-dimensional compressible Euler equations with Furusawa and Togashi's nuclear equation of state. We focus on the prompt convection at ∼10 ms after bounce and investigate how neutrinos are transported in the convective matter. We apply a new analysis based on the eigenvalues and eigenvectors of the Eddington tensor and make a comparison between the Boltzmann transport results and the M1 closure approximation in the transition regime between the optically thick and thin limits. We visualize the eigenvalues and eigenvectors using an ellipsoid, in which each principal axis is parallel to one of the eigenvectors and has a length proportional to the corresponding eigenvalue. This approach enables us to understand the difference between the Eddington tensor derived directly from the Boltzmann simulation and the one given by the M1 prescription from a new perspective. We find that the longest principal axis of the ellipsoid is almost always nearly parallel to the energy flux in the M1 closure approximation, whereas in the Boltzmann simulation it becomes perpendicular in some transition regions, where the mean free path is ∼0.1 times the radius. In three spatial dimensions, the convective motions make it difficult to predict where this happens and to possibly improve the closure relation there.

Using the Boltzmann-radiation-hydrodynamics code, which solves the Boltzmann equation for neutrino transport, we present the results of the simulations with the nuclear equations of state (EOSs) of Lattimer and Swesty (LS) and Furusawa and Shen (FS). We extend the simulation time of the LS model and conduct thorough investigations, though our previous paper briefly reported some of the results. Only the LS model shows the shock revival. This seems to originate from the nuclear composition: the different nuclear composition results in the different energy loss by photodissociation and hence the different strength of the prompt convection and the later neutrino-driven convection. The protoneutron star seen in the FS model is more compact than that in the LS model because the existence of multinuclear species softens the EOS. For the behavior of neutrinos, we examined the flux and the Eddington tensor of neutrinos. In the optically thick region, the diffusion of neutrinos and the dragging by the motion of matter determine the flux. In the optically thin region, the free-streaming determines it. The Eddington tensor is compared with that obtained from the M1-closure relation. The M1-closure scheme overestimates the contribution from the velocity-dependent terms in the semitransparent region.

We perform (3+1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal superhorizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for large amplitude of perturbations expected for PBH formation.

© 2020 American Physical Society. We study gravitational waves from a hierarchical three-body system up to first-order post-Newtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner binary and relative inclination, known as Kozai-Lidov oscillations. We analyze features of the waveform from the inner binary system undergoing such oscillations. We find that variation caused due to the tertiary companion can be observed in the gravitational waveforms and energy spectra, which should be compared with those from isolated binaries and coplanar three-body system. The detections from future space-based interferometers will make possible the investigation of gravitational wave spectrum in mHz range and may fetch signals by sources addressed.

© 2019 American Physical Society. Neutrinos are densely populated deep inside the core of massive stars after their gravitational collapse to produce supernova explosions and form compact stars such as neutron stars and black holes. It has been considered that they may change their flavor identities through so-called fast-pairwise conversions induced by mutual forward scatterings. If that is really the case, the dynamics of supernova explosion will be influenced, since the conversion may occur near the neutrino sphere, from which neutrinos are effectively emitted. In this paper, we conduct a pilot study of such possibilities based on the results of fully self-consistent, realistic simulations of a core-collapse supernova explosion in two spatial dimensions under axisymmetry. As we solved the Boltzmann equations for neutrino transfer in the simulation not as a postprocess but in real time, the angular distributions of neutrinos in momentum space for all points in the core at all times are available, a distinct feature of our simulations. We employ some of these distributions extracted at a few selected points and times from the numerical data and apply linear analysis to assess the possibility of the conversion. We focus on the vicinity of the neutrino sphere, where different species of neutrinos move in different directions and have different angular distributions as a result. This is a pilot study for a more thorough survey that will follow soon. We find no positive sign of conversion unfortunately at least for the spatial points and times we studied in this particular model. We hence investigate rather in detail the condition for the conversion by modifying the neutrino distributions rather arbitrarily by hand.

© 2019 IOP Publishing Ltd. Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. We construct the initial data for a Gaussian-like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. It is shown that the expansion law in a late time approaches that of the radiation dominated universe and the matter dominated universe for the small and large initial amplitude cases, respectively. For the large initial amplitude case, the horizon is initially a past outer trapping horizon, whose area decreases with time, and after a certain period of time, it turns to a future outer trapping horizon with the increasing area.

© 2019. The American Astronomical Society. All rights reserved. With the Boltzmann-radiation-hydrodynamics code, which we have developed to solve numerically the Boltzmann equations for neutrino transfer, the Newtonian hydrodynamics equations, and the Newtonian self-gravity simultaneously and consistently, we simulate the collapse of a rotating core of the progenitor with a zero-age- main-sequence mass of 11.2 M and a shellular rotation of at the center. We pay particular attention in this paper to the neutrino distribution in phase space, which is affected by the rotation. By solving the Boltzmann equations directly, we can assess the rotation-induced distortion of the angular distribution in momentum space, which gives rise to the rotational component of the neutrino flux. We compare the Eddington tensors calculated both from the raw data and from the M1-closure approximation. We demonstrate that the Eddington tensor is determined by complicated interplays of the fluid velocity and the neutrino interactions and that the M1-closure, which assumes that the Eddington factor is determined by the flux factor, fails to fully capture this aspect, especially in the vicinity of the shock. We find that the error in the Eddington factor reaches ∼20% in our simulation. This is due not to the resolution but to the different dependence of the Eddington and flux factors on the angular profile of the neutrino distribution function, and hence modification to the closure relation is needed.

© 2019. The American Astronomical Society. All rights reserved.. We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that approximately describe accretion flows through a standing shock wave onto a protoneutron star and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the two-dimensional steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star is rotating and/or has a magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force, and the critical luminosity is modified. In fact, we find that the critical luminosity is reduced by about 50%-70% for very rapid rotations; the rotation frequencies are 0.2-0.45 s -1 at the radius of r = 1000 km (equivalent to spin periods ∼0.5-0.22 ms at r = 10 km) and about 20%-50% for strong toroidal magnetic fields (the strengths of which are 1.0 × 10 12 -3.0 × 10 12 G at r = 1000 km), depending on the mass accretion rate. These results may also be interpreted as the existence of a critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will be revived for a given combination of mass accretion rate and neutrino luminosity.

With the Boltzmann-radiation-hydrodynamics code, which we have developed to<br />
solve numerically the Boltzmann equations for neutrino transfer, the Newtonian<br />
hydrodynamics equations, and the Newtonian self-gravity simultaneously and<br />
consistently, we simulate the collapse of a rotating core of the progenitor<br />
with a zero-age-main-sequence mass of $11.2\,M_\odot$ and a shelluler rotation<br />
of $1\,{\rm rad\,s^{-1 } }$ at the center. We pay particular attention in this<br />
paper to the neutrino distribution in phase space, which is affected by the<br />
rotation. By solving the Boltzmann equations directly, we can assess the<br />
rotation-induced distortion of the angular distribution in momentum space,<br />
which gives rise to the rotational component of the neutrino flux. We compare<br />
the Eddington tensors calculated both from the raw data and from the M1-closure<br />
approximation. We demonstrate that the Eddington tensor is determined by<br />
complicated interplays of the fluid velocity and the neutrino interactions, and<br />
that the M1-closure, which assumes that the Eddington factor is determined by<br />
the flux factor, fails to fully capture this aspect especially in the vicinity<br />
of the shock. We find that the error in the Eddington factor reaches $\sim<br />
20\%$ in our simulation. This is due to not the resolution but different<br />
dependence of the Eddington and flux factors on the angular profile of the<br />
neutrino distribution function and hence modification to the closure relation<br />
is needed.

© 2018 American Physical Society. We analyze the collisional Penrose process of spinning test particles in an extreme Kerr black hole. We consider that two particles plunge into the black hole from infinity and collide near the black hole. For the collision of two massive particles, if the spins of particles are s1≈0.01379 μM and s2≈-0.2709 μM, we obtain the maximal efficiency is about ηmax=(extracted energy)/(input energy)≈15.01, which is more than twice as large as the case of the collision of non-spinning particles (ηmax≈6.32). We also evaluate the collision of a massless particle without spin and a massive particle with spin (Compton scattering), in which we find the maximal efficiency is ηmax≈26.85 when s2≈-0.2709 μM, which should be compared with ηmax≈13.93 for the nonspinning case.

We investigate axisymmetric steady solutions of (magneto)hydrodynamics<br />
equations that describe approximately accretion flows through a standing shock<br />
wave and discuss the effects of rotation and magnetic field on the revival of<br />
the stalled shock wave in supernova explosions. We develop a new powerful<br />
numerical method to calculate the 2-dimensional (2D) steady accretion flows<br />
self-consistently. We first confirm the results of preceding papers that there<br />
is a critical luminosity of irradiating neutrinos, above which there exists no<br />
steady solution in spherical models. If a collapsing star has rotation and/or<br />
magnetic field, the accretion flows are no longer spherical owing to the<br />
centrifugal force and/or Lorentz force and the critical luminosity is<br />
modified.In fact we find that the critical luminosity is reduced by about 50% -<br />
70% for rapid rotations and about 20% - 50% for strong toroidal magnetic<br />
fields, depending on the mass accretion rate. These results may be also<br />
interpreted as an existence of the critical specific angular momentum or<br />
critical magnetic field, above which there exists no steady solution and the<br />
standing shock wave will revive for a given combination of mass accretion rate<br />
and neutrino luminosity.

We propose a new class of method for solving nonlinear systems of equations,<br />
which, among other things,has four nice features: (i) it is inspired by the<br />
mathematical property of damped oscillators, (ii) it can be regarded as a<br />
simple extention to the Newton-Raphson(NR) method, (iii) it has the same local<br />
convergence as the NR method does, (iv) it has a significantly wider<br />
convergence region or the global convergence than that of the NR method. In<br />
this article, we present the evidence of these properties, applying our new<br />
method to some examples and comparing it with the NR method.

© 2018. The American Astronomical Society. We present the first results of our spatially axisymmetric core-collapse supernova simulations with full Boltzmann neutrino transport, which amount to a time-dependent five-dimensional (two in space and three in momentum space) problem. Special relativistic effects are fully taken into account with a two-energy-grid technique. We performed two simulations for a progenitor of 11.2 M⊙, employing different nuclear equations of state (EOSs): Lattimer and Swesty's EOS with the incompressibility of K =220 MeV (LS EOS) and Furusawa's EOS based on the relativistic mean field theory with the TM1 parameter set (FS EOS). In the LS EOS, the shock wave reaches ∼700 km at 300 ms after bounce and is still expanding, whereas in the FS EOS it stalled at ∼200 km and has started to recede by the same time. This seems to be due to more vigorous turbulent motions in the former during the entire postbounce phase, which leads to higher neutrino-heating efficiency in the neutrino-driven convection. We also look into the neutrino distributions in momentum space, which is the advantage of the Boltzmann transport over other approximate methods. We find nonaxisymmetric angular distributions with respect to the local radial direction, which also generate off-diagonal components of the Eddington tensor. We find that the rθ component reaches ∼10% of the dominant rr component and, more importantly, it dictates the evolution of lateral neutrino fluxes, dominating over the θθ component, in the semitransparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.

© 2018 authors. Published by the American Physical Society. We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j=2, =0 as well as a spherically symmetric solution with j=0, =2 in this system where j is the total angular momentum quantum number and is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

© The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. Energy extraction from a rotating or charged black hole is one of the fascinating issues in general relativity. The collisional Penrose process is one such extraction mechanism and has been reconsidered intensively since Bañados, Silk, and West pointed out the physical importance of very high energy collisions around a maximally rotating black hole. In order to get results analytically, the test particle approximation has been adopted so far. Successive works based on this approximation scheme have not yet revealed the upper bound on the efficiency of the energy extraction because of the lack of backreaction. In the Reissner-Nordström spacetime, by fully taking into account the self-gravity of the shells, we find that there is an upper bound on the extracted energy that is consistent with the area law of a black hole. We also show one particular scenario in which almost the maximum energy extraction is achieved even without the Bañados-Silk-West collision.

© 2017 IOP Publishing Ltd. We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky (ST) (1991 Phys. Rev. Lett. 66 994). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but goes well beyond. We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.

© 2016 American Physical Society. A new computationally efficient method has been introduced to treat self-gravity in Eulerian hydrodynamical simulations. It is applied simply by modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method cannot only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids, and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.

© 2016 American Physical Society. We provide a detailed analysis of how bosonic dark matter "condensates" interact with compact stars, extending significantly the results of a recent Letter [1]. We focus on bosonic fields with mass mB, such as axions, axion-like candidates and hidden photons. Self-gravitating bosonic fields generically form "breathing" configurations, where both the spacetime geometry and the field oscillate, and can interact and cluster at the center of stars. We construct stellar configurations formed by a perfect fluid and a bosonic condensate, and which may describe the late stages of dark matter accretion onto stars, in dark-matter-rich environments. These composite stars oscillate at a frequency which is a multiple of f=2.5×1014(mBc2/eV) Hz. Using perturbative analysis and numerical relativity techniques, we show that these stars are generically stable, and we provide criteria for instability. Our results also indicate that the growth of the dark matter core is halted close to the Chandrasekhar limit. We thus dispel a myth concerning dark matter accretion by stars: dark matter accretion does not necessarily lead to the destruction of the star, nor to collapse to a black hole. Finally, we argue that stars with long-lived bosonic cores may also develop in other theories with effective mass couplings, such as (massless) scalar-tensor theories.

© 2015 IOP Publishing Ltd. One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

� 2015 IOP Publishing Ltd. Black holes are a laboratory not only for testing the theory of gravity but also for exploring the properties of fundamental fields. Fundamental fields around a supermassive black hole give rise to extremely long-lived quasi-bound states which can in principle extract the energy and angular momentum from the black hole. To investigate the final state of such a system, the backreaction onto the spacetime becomes important because of the nonlinearity of the Einstein equation. In this paper, we review the numerical method to trace the evolution of massive scalar fields in the vicinity of black holes, how such a system originates from scalar clouds initially in the absence of black holes or from the capture of scalar clouds by a black hole, and the evolution of quasi-bound states around both a non-rotating black hole and a rotating black hole including the backreaction.

© 2015 American Physical Society. Searches for dark matter imprints are one of the most active areas of current research. We focus here on light fields with mass mB, such as axions and axionlike candidates. Using perturbative techniques and full-blown nonlinear numerical relativity methods, we show the following. (i) Dark matter can pile up in the center of stars, leading to configurations and geometries oscillating with a frequency that is a multiple of f=2.5×1014(mBc2/eV)Hz. These configurations are stable throughout most of the parameter space, and arise out of credible mechanisms for dark-matter capture. Stars with bosonic cores may also develop in other theories with effective mass couplings, such as (massless) scalar-tensor theories. We also show that (ii) collapse of the host star to a black hole is avoided by efficient gravitational cooling mechanisms.

© 2015 American Physical Society. We investigate properties of material ejected dynamically in the merger of black hole-neutron star binaries by numerical-relativity simulations. We systematically study the dependence of ejecta properties on the mass ratio of the binary, spin of the black hole, and equation of state of the neutron-star matter. Dynamical mass ejection is driven primarily by tidal torque, and the ejecta is much more anisotropic than that from binary neutron star mergers. In particular, the dynamical ejecta is concentrated around the orbital plane with a half opening angle of 10°-20° and often sweeps out only a half of the plane. The ejecta mass can be as large as ∼0.1M, and the velocity is subrelativistic with ∼0.2-0.3c for typical cases. The ratio of the ejecta mass to the bound mass (disk and fallback components) is larger, and the ejecta velocity is larger, for larger values of the binary mass ratio, i.e., for larger values of the black-hole mass. The remnant black hole-disk system receives a kick velocity of O(100)kms-1 due to the ejecta linear momentum, and this easily dominates the kick velocity due to gravitational radiation. Structures of postmerger material, velocity distribution of the dynamical ejecta, fallback rates, and gravitational waves are also investigated. We also discuss the effect of ejecta anisotropy on electromagnetic counterparts, specifically a macronova/kilonova and synchrotron radio emission, developing analytic models.

© 2015 World Scientific Publishing Company. Gravitational compact astrophysical objects are excellent laboratories to test the strong field regime of theories of gravity. Among these compact objects, lies the ultracompact class: stellar structures that possess a light ring (circular null geodesic). Such ultracompact stars were presented in literature in the earlier solutions of general relativity, and some are claimed to be good candidates to the supermassive objects present at the center of galaxies. In this paper, we present evidences for the claim that compact objects with a light ring should be black holes, based on the existence of long-lived modes obtained through a first-order perturbation theory. These first-order long-lived modes can source nonlinear terms which could turn the star unstable. We show, in particular, a comparison between modes computed through an exact direct integration and through the WKB approximation. Moreover, we present the time evolution of wavepackets for different field configurations. We conjecture some possible outcomes of the nonlinear instability. The discussion presented in this work complements our previous paper [Phys. Rev. D90 (2014) 044069].

We investigate properties of material ejected dynamically in the merger of black hole-neutron star binaries by numerical-relativity simulations. We systematically study the dependence of ejecta properties on the mass ratio of the binary, spin of the black hole, and equation of state of the neutron-star matter. Dynamical mass ejection is driven primarily by tidal torque, and the ejecta is much more anisotropic than that from binary neutron star mergers. In particular, the dynamical ejecta is concentrated around the orbital plane with a half opening angle of 10 degrees-20 degrees and often sweeps out only a half of the plane. The ejecta mass can be as large as similar to 0.1M(circle dot), and the velocity is subrelativistic with similar to 0.2-0.3c for typical cases. The ratio of the ejecta mass to the bound mass (disk and fallback components) is larger, and the ejecta velocity is larger, for larger values of the binary mass ratio, i.e., for larger values of the black-hole mass. The remnant black hole-disk system receives a kick velocity of O(100) km s(-1) due to the ejecta linear momentum, and this easily dominates the kick velocity due to gravitational radiation. Structures of postmerger material, velocity distribution of the dynamical ejecta, fallback rates, and gravitational waves are also investigated. We also discuss the effect of ejecta anisotropy on electromagnetic counterparts, specifically a macronova/kilonova and synchrotron radio emission, developing analytic models.

© 2015 American Physical Society. We systematically performed numerical-relativity simulations for black hole-neutron star (BH-NS) binary mergers with a variety of the BH spin orientation and nuclear-theory-based equations of state (EOS) of the NS. The initial misalignment angles of the BH spin measured from the direction of the orbital angular momentum are chosen in the range of itilt,0≈30°-90°. We employed four models of nuclear-theory-based zero-temperature EOS for the NS in which the compactness of the NS is in the range of C=MNS/RNS=0.138-0.180, where MNS and RNS are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, Q=MBH/MNS, and the dimensionless spin parameter of the BH, χ, are chosen to be Q=5 and χ=0.75, together with MNS=1.35M so that the BH spin misalignment has a significant effect on tidal disruption of the NS. We obtain the following results: (i) The inclination angles of itilt,0<70° and itilt,0<50° are required for the formation of a remnant disk with its mass larger than 0.1M for the cases C=0.140 and C=0.160, respectively, while the disk mass is always smaller than 0.1M for C0.175. The ejecta with its mass larger than 0.01M is obtained for itilt,0<85° with C=0.140, for itilt,0<65° with C=0.160, and for itilt,0<30° with C=0.175. (ii) The rotational axis of the dense part of the remnant disk with its rest-mass density larger than 109g/cm3 is approximately aligned with the remnant BH spin for itilt,0≈30°. On the other hand, the disk axis is misaligned initially with ∼30° for itilt,0≈60°, and the alignment with the remnant BH spin is achieved at ∼50-60ms after the onset of merger. The accretion time scale of the remnant disk is typically ∼100ms and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically ∼0.2-0.3c and depends only weakly on the misalignment angle and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for itilt,0?60°.

We systematically performed numerical-relativity simulations for black hole-neutron star (BH-NS) binary mergers with a variety of the BH spin orientation and nuclear-theory-based equations of state (EOS) of the NS. The initial misalignment angles of the BH spin measured from the direction of the orbital angular momentum are chosen in the range of i(tilt,0) approximate to 30 degrees - 90 degrees. We employed four models of nuclear-theory-based zero-temperature EOS for the NS in which the compactness of the NS is in the range of C = M-NS/R-NS = 0.138 - 0.180, where M-NS and R-NS are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, Q = M-BH/M-NS, and the dimensionless spin parameter of the BH, chi, are chosen to be Q = 5 and chi = 0.75, together with M-NS = 1.35M(circle dot) so that the BH spin misalignment has a significant effect on tidal disruption of the NS. We obtain the following results: (i) The inclination angles of i(tilt,0) &lt; 70 degrees and i(tilt,0) &lt; 50 degrees are required for the formation of a remnant disk with its mass larger than 0.1M(circle dot) for the cases C = 0.140 and C = 0.160, respectively, while the disk mass is always smaller than 0.1M(circle dot) for C greater than or similar to 0.175. The ejecta with its mass larger than 0.01M(circle dot) is obtained for i(tilt,0) &lt; 85 degrees with C = 0.140, for i(tilt,0) &lt; 65 degrees with C = 0.160, and for i(tilt,0) &lt; 30 degrees with C = 0.175. (ii) The rotational axis of the dense part of the remnant disk with its rest-mass density larger than 10(9) g/cm(3) is approximately aligned with the remnant BH spin for i(tilt,0) approximate to 30 degrees. On the other hand, the disk axis is misaligned initially with similar to 30 degrees for i(tilt,0) approximate to 60 degrees, and the alignment with the remnant BH spin is achieved at similar to 50-60 ms after the onset of merger. The accretion time scale of the remnant disk is typically similar to 100 ms and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically similar to 0.2-0.3c and depends only weakly on the misalignment angle and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for i(tilt,0) less than or similar to 60 degrees.

© 2015 American Physical Society. We perform new long-term (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order, and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than one radian. We then compare the extrapolated waveforms with those calculated by the latest effective-one-body (EOB) formalism in which the so-called tidal deformability, higher post-Newtonian corrections, and gravitational self-force effects are taken into account. We show that for a binary of compact neutron stars with their radius 11.1 km, the waveform by the EOB formalism agrees quite well with the numerical waveform so that the total phase error is smaller than one radian for the total phase of ∼200 radian up to the merger. By contrast, for a binary of less compact neutron stars with their radius 13.6 km, the EOB and numerical waveforms disagree with each other in the last few wave cycles, resulting in the total phase error of approximately three radian.

We perform new long-term (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order, and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than one radian. We then compare the extrapolated waveforms with those calculated by the latest effective-one-body (EOB) formalism in which the so-called tidal deformability, higher post-Newtonian corrections, and gravitational self-force effects are taken into account. We show that for a binary of compact neutron stars with their radius 11.1 km, the waveform by the EOB formalism agrees quite well with the numerical waveform so that the total phase error is smaller than one radian for the total phase of similar to 200 radian up to the merger. By contrast, for a binary of less compact neutron stars with their radius 13.6 km, the EOB and numerical waveforms disagree with each other in the last few wave cycles, resulting in the total phase error of approximately three radian.

© 2014 American Physical Society. Scalar fields pervade theoretical physics and are a fundamental ingredient to solve the dark matter problem, to realize the Peccei-Quinn mechanism in QCD or the string-axiverse scenario. They are also a useful proxy for more complex matter interactions, such as accretion disks or matter in extreme conditions. Here, we study the collision between scalar "clouds" and rotating black holes. For the first time we are able to compare analytic estimates and strong field, nonlinear numerical calculations for this problem. As the black hole pierces through the cloud it accretes according to the Bondi-Hoyle prediction, but is deflected through a purely kinematic gravitational "anti-Magnus" effect, which we predict to be present also during the interaction of black holes with accretion disks. After the interaction is over, we find large recoil velocities in the transverse direction. The end-state of the process belongs to the vacuum Kerr family if the scalar is massless, but can be a hairy black hole when the scalar is massive.

© 2014 American Physical Society. The discovery of a "weakly turbulent" instability of anti-de Sitter spacetime supports the idea that confined fluctuations eventually collapse to black holes and suggests that similar phenomena might be possible in asymptotically flat spacetime, for example in the context of spherically symmetric oscillations of stars or nonradial pulsations of ultracompact objects. Here we present a detailed study of the evolution of the Einstein-Klein-Gordon system in a cavity, with different types of deformations of the spectrum, including a mass term for the scalar and Neumann conditions at the boundary. We provide numerical evidence that gravitational collapse always occurs, at least for amplitudes that are three orders of magnitude smaller than Choptuik's critical value and corresponding to more than 105 reflections before collapse. The collapse time scales as the inverse square of the initial amplitude in the small-amplitude limit. In addition, we find that fields with nonresonant spectrum collapse earlier than in the fully resonant case, a result that is at odds with the current understanding of the process. Energy is transferred through a direct cascade to high frequencies when the spectrum is resonant, but we observe both direct- and inverse-cascade effects for nonresonant spectra. Our results indicate that a fully resonant spectrum might not be a crucial ingredient of the conjectured turbulent instability and that other mechanisms might be relevant. We discuss how a definitive answer to this problem is essentially impossible within the present framework.

© 2014 American Physical Society. The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods." In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to the collision from rest of two equal-mass black holes. We calculate the total radiated energy to be Erad/M=(9.0±0.5)×10-4 in five dimensions and Erad/M=(8.1±0.4)×10-4 in six dimensions.

Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the "black hole hypothesis," once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we explore in some depth the mode structure of ultracompact stars, in particular constant-density stars and gravastars. We show that the existence of very long-lived modes - localized near a second, stable null geodesic - is a generic feature of gravitational perturbations of such configurations. Already at the linear level, such modes become unstable if the object rotates sufficiently fast to develop an ergoregion. Finally, we conjecture that the long-lived modes become unstable under fragmentation via a Dyson-Chandrasekhar-Fermi mechanism at the nonlinear level. Depending on the structure of the star, it is also possible that nonlinearities lead to the formation of small black holes close to the stable light ring. Our results suggest that the mere observation of a light ring is a strong evidence for the existence of black holes. © 2014 American Physical Society.

Time evolution of a black hole lattice universe with a positive cosmological constant Λ is simulated. The vacuum Einstein equations are numerically solved in a cubic box with a black hole in the center. Periodic boundary conditions on all pairs of opposite faces are imposed. Configurations of marginally trapped surfaces are analyzed. We describe the time evolution of not only black hole horizons, but also cosmological horizons. Defining the effective scale factor by using the area of a surface of the cubic box, we compare it with that in the spatially flat dust dominated Friedmann- Lemaître-Robertson-Walker (FLRW) universe with the same value of Λ. It is found that the behavior of the effective scale factor is well approximated by that in the FLRW universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the Universe irrespective of the value of Λ. © 2014 American Physical Society.

Fundamental fields are a natural outcome in cosmology and particle physics and might therefore serve as a proxy for more complex interactions. The equivalence principle implies that all forms of matter gravitate, and one therefore expects relevant, universal imprints of new physics in strong field gravity, such as that encountered close to black holes. Fundamental fields in the vicinities of supermassive black holes give rise to extremely long-lived, or even unstable, configurations, which slowly extract angular momentum from the black hole or simply evolve nonlinearly over long time scales, with important implications for particle physics and gravitational-wave physics. Here, we perform a fully nonlinear study of scalar-field condensates around rotating black holes. We provide novel ways to specify initial data for the Einstein - Klein - Gordon system, with potential applications in a variety of scenarios. Our numerical results confirm the existence of long-lived bar modes, which act as lighthouses for gravitational wave emission: the scalar field condenses outside the black hole geometry and acts as a constant frequency gravitational-wave source for very long time scales. This effect could turn out to be a potential signature of beyond standard model physics and also a promising source of gravitational waves for future gravitational-wave detectors. © 2014 American Physical Society.

Fundamental fields are a natural outcome in cosmology and particle physics and might therefore serve as a proxy for more complex interactions. The equivalence principle implies that all forms of matter gravitate, and one therefore expects relevant, universal imprints of new physics in strong field gravity, such as that encountered close to black holes. Fundamental fields in the vicinities of supermassive black holes give rise to extremely long-lived, or even unstable, configurations, which slowly extract angular momentum from the black hole or simply evolve nonlinearly over long time scales, with important implications for particle physics and gravitational-wave physics. Here, we perform a fully nonlinear study of scalar-field condensates around rotating black holes. We provide novel ways to specify initial data for the Einstein-Klein-Gordon system, with potential applications in a variety of scenarios. Our numerical results confirm the existence of long-lived bar modes, which act as lighthouses for gravitational wave emission: the scalar field condenses outside the black hole geometry and acts as a constant frequency gravitational-wave source for very long time scales. This effect could turn out to be a potential signature of beyond standard model physics and also a promising source of gravitational waves for future gravitational-wave detectors.

We carry out numerical-relativity simulations of coalescing binary neutron stars in a scalar-tensor theory that admits spontaneous scalarization. We model neutron stars with realistic equations of state. We choose the free parameters of the theory taking into account the constraints imposed by the latest observations of neutron-star-white-dwarf binaries with pulsar timing. We show that even within those severe constraints, scalarization can still affect the evolution of the binary neutron stars, not only during the late inspiral but also during the merger stage. We also confirm that even when both neutron stars have quite small scalar charge at large separations, they can be strongly scalarized dynamically during the final stages of the inspiral. In particular, we identify the binary parameters for which scalarization occurs either during the late inspiral or only after the onset of the merger when a remnant, supramassive, or hypermassive neutron star is formed. We also discuss how those results can impact the extraction of physical information on gravitational waves once they are detected. © 2014 American Physical Society.

The nonlinear instability of anti-de Sitter spacetime has recently been established with the striking result that generic initial data collapse to form black holes. This outcome suggests that confined matter might generically collapse, and that collapse could only be halted - at most - by nonlinear bound states. Here, we provide evidence that such a mechanism can operate even in asymptotically flat spacetimes by studying the evolution of the Einstein-Klein-Gordon system for a self-interacting scalar field. We show that (i) configurations which do not collapse promptly can do so after successive reflections off the potential barrier, but (ii) that at intermediate amplitudes and Compton wavelengths, collapse to black holes is replaced by the appearance of oscillating soliton stars, or "oscillatons." Finally, (iii) for very small initial amplitudes, the field disperses away in a manner consistent with power-law tails of massive fields. Minkowski is stable against gravitational collapse. Our results provide one further piece to the rich phenomenology of gravitational collapse and show the important interplay between bound states, blueshift, dissipation and confinement effects. © 2014 American Physical Society.

Stationary pulsar magnetospheres in the force-free system are governed by the pulsar equation. In 1999, Contopoulos, Kazanas, and Fendt (hereafter CKF) numerically solved the pulsar equation and obtained a pulsar magnetosphere model called the CKF solution that has both closed and open magnetic field lines. The CKF solution is a successful solution, but it contains a poloidal current sheet that flows along the last open field line. This current sheet is artificially added to make the current system closed. In this paper, we suggest an alternative method to solve the pulsar equation and construct pulsar magnetosphere models without a current sheet. In our method, the pulsar equation is decomposed into Ampère's law and the force-free condition. We numerically solve these equations simultaneously with a fixed poloidal current. As a result, we obtain a pulsar magnetosphere model without a current sheet, which is similar to the CKF solution near the neutron star and has a jet-like structure at a distance along the pole. In addition, we discuss physical properties of the model and find that the force-free condition breaks down in a vicinity of the light cylinder due to dissipation that is included implicitly in the numerical method. © The Author 2014. Published by Oxford University Press on behalf of the Astronomical Society of Japan. All rights reserved.

Time evolution of a black hole lattice toy model universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of faces opposite to each other. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-de Sitter universe. It is found that the behavior of the effective scale factors is well approximated by that in the Einstein-de Sitter universe. In our model, if the box size is sufficiently larger than the horizon radius, local inhomogeneities do not significantly affect the global expansion law of the Universe even though the inhomogeneity is extremely nonlinear. © 2013 American Physical Society.

Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to evolve such systems, a proper understanding of the methods involved is quite important. Here, we focus on the numerical solution of elliptic partial differential equations. Such equations arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes. Because such elliptic equations play an important role in many branches of physics, we give an overview of the topic, and show how to numerically solve them with simple examples and sample codes written in C++ and Fortran90 for beginners in numerical relativity or other fields requiring numerical expertise. © 2013 World Scientific Publishing Company.

Numerical-relativity simulations for the merger of binary neutron stars are performed for a variety of equations of state (EOSs) and for a plausible range of the neutron-star mass, focusing primarily on the properties of the material ejected from the system. We find that a fraction of the material is ejected as a mildly relativistic and mildly anisotropic outflow with the typical and maximum velocities ∼0.15-0.25c and ∼0.5-0.8c (where c is the speed of light), respectively, and that the total ejected rest mass is in a wide range 10 -4-10-2M⊙, which depends strongly on the EOS, the total mass, and the mass ratio. The total kinetic energy ejected is also in a wide range between 1049 and 1051 ergs. The numerical results suggest that for a binary of canonical total mass 2.7M ⊙, the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the r-process or through the formation of blast waves during the interaction with the interstellar matter, if the EOS and mass of the binary are favorable ones. © 2013 American Physical Society.

Physic in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high-energy physics (HEP). The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong-field astrophysical processes, could prove extremely useful to understand HEP processes such as trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with a roadmap for the next years. © 2012 IOP Publishing Ltd.

We study the merger of black hole-neutron star binaries with a variety of black hole spins aligned or antialigned with the orbital angular momentum, and with the mass ratio in the range MBH/MNS=2-5, where M BH and MNS are the mass of the black hole and neutron star, respectively. We model neutron-star matter by systematically parametrized piecewise polytropic equations of state. The initial condition is computed in the puncture framework adopting an isolated horizon framework to estimate the black hole spin and assuming an irrotational velocity field for the fluid inside the neutron star. Dynamical simulations are performed in full general relativity by an adaptive-mesh refinement code, SACRA. The treatment of hydrodynamic equations and estimation of the disk mass are improved. We find that the neutron star is tidally disrupted irrespective of the mass ratio when the black hole has a moderately large prograde spin, whereas only binaries with low mass ratios, MBH/MNS3, or small compactnesses of the neutron stars bring the tidal disruption when the black hole spin is zero or retrograde. The mass of the remnant disk is accordingly large as <0.1M ™, which is required by central engines of short gamma-ray bursts, if the black hole spin is prograde. Information of the tidal disruption is reflected in a clear relation between the compactness of the neutron star and an appropriately defined "cutoff frequency" in the gravitational-wave spectrum, above which the spectrum damps exponentially. We find that the tidal disruption of the neutron star and excitation of the quasinormal mode of the remnant black hole occur in a compatible manner in high mass-ratio binaries with the prograde black hole spin. The correlation between the compactness and the cutoff frequency still holds for such cases. It is also suggested by extrapolation that the merger of an extremely spinning black hole and an irrotational neutron star binary does not lead to the formation of an overspinning black hole. © 2011 American Physical Society.

We study the merger of black hole-neutron star binaries with a variety of black hole spins aligned or antialigned with the orbital angular momentum, and with the mass ratio in the range M-BH/M-NS = 2-5, where M-BH and M-NS are the mass of the black hole and neutron star, respectively. We model neutron-star matter by systematically parametrized piecewise polytropic equations of state. The initial condition is computed in the puncture framework adopting an isolated horizon framework to estimate the black hole spin and assuming an irrotational velocity field for the fluid inside the neutron star. Dynamical simulations are performed in full general relativity by an adaptive-mesh refinement code, SACRA. The treatment of hydrodynamic equations and estimation of the disk mass are improved. We find that the neutron star is tidally disrupted irrespective of the mass ratio when the black hole has a moderately large prograde spin, whereas only binaries with low mass ratios, M-BH/M-NS less than or similar to 3, or small compactnesses of the neutron stars bring the tidal disruption when the black hole spin is zero or retrograde. The mass of the remnant disk is accordingly large as greater than or similar to 0.1M(circle dot), which is required by central engines of short gamma-ray bursts, if the black hole spin is prograde. Information of the tidal disruption is reflected in a clear relation between the compactness of the neutron star and an appropriately defined "cutoff frequency" in the gravitational-wave spectrum, above which the spectrum damps exponentially. We find that the tidal disruption of the neutron star and excitation of the quasinormal mode of the remnant black hole occur in a compatible manner in high mass-ratio binaries with the prograde black hole spin. The correlation between the compactness and the cutoff frequency still holds for such cases. It is also suggested by extrapolation that the merger of an extremely spinning black hole and an irrotational neutron star binary does not lead to the formation of an overspinning black hole.

We perform a numerical-relativity simulation for the merger of binary neutron stars with 6 nuclear-theory-based equations of states (EOSs) described by piecewise polytropes. Our purpose is to explore the dependence of the dynamical behavior of the binary neutron star merger and resulting gravitational waveforms on the EOS of the supernuclear-density matter. The numerical results show that the merger process and the first outcome are classified into three types: (i) a black hole is promptly formed, (ii) a short-lived hypermassive neutron star (HMNS) is formed, (iii) a long-lived HMNS is formed. The type of the merger depends strongly on the EOS and on the total mass of the binaries. For the EOS with which the maximum mass is larger than 2M, the lifetime of the HMNS is longer than 10ms for a total mass m0=2.7M. A recent radio observation suggests that the maximum mass of spherical neutron stars is M max 1.97±0.04M in one σ level. This fact and our results support the possible existence of a HMNS soon after the onset of the merger for a typical binary neutron star with m0=2.7M. We also show that the torus mass surrounding the remnant black hole is correlated with the type of the merger process; the torus mass could be large, 0.1M, in the case that a long-lived HMNS is formed. We also show that gravitational waves carry information of the merger process, the remnant, and the torus mass surrounding a black hole. © 2011 American Physical Society.

It may be widely believed that probing short distance physics is limited by the presence of the Planck energy scale above which scale any information is cloaked behind a horizon. If this hypothesis is correct, we could observe quantum behavior of gravity only through a black hole of Planck mass. We numerically show that in a scattering of two black holes in the 5-dimensional spacetime, a visible domain, whose curvature radius is much shorter than the Planck length, can be formed. Our result indicates that super-Planckian phenomena may be observed without an obstruction by horizon formation in particle accelerators. © 2011 American Physical Society.

We study the high-velocity collision of two black holes in five dimension by numerical relativity. We prepare two boosted black holes for the initial condition and perform simulations for two equal mass black holes of no spin. We show some results of five-dimensional simulations compared with four-dimensional simulations.

We study the high-velocity collision of two black holes in five dimension by numerical relativity. We prepare two boosted black holes for the initial condition and perform simulations for two equal mass black holes of no spin. We show some results of five-dimensional simulations compared with four-dimensional simulations.

We report our recent results obtained from numerical-relativity simulations of black hole-neutron star binary mergers with a variety of equations of state and black hole spins. The tidal disruption of the neutron star occurs even for high mass-ratio binaries of MBH/MNS = 5, if the black hole has a sufficiently large prograde spin. Information about the equation of state at high density can be obtained from observations of gravitational waves, especially from the cutoff frequency shown in the spectra.

We study nonaxisymmetric collision of two black holes (BHs) with a high velocity v=|dxi/dx0|=0.6c-0.9c at infinity, where xμ denotes four-dimensional coordinates. We prepare two boosted BHs for the initial condition which is different from that computed by a simple moving-puncture approach. By extrapolation of the numerical results, we find that the impact parameter has to be smaller than 2.5GM0/c2 for formation of a BH in the collision for v→c, where M0c2 is the initial total Arnowitt-Deser-Misner energy of the system. For the critical value of the impact parameter, 20%-30% of mass energy and 60%-70% of angular momentum are dissipated by gravitational radiation for v=0.6c-0.9c. © 2008 The American Physical Society.