Numerical relativity has recently yielded a plethora of results about kicks from spinning mergers which has, in turn, vastly increased our knowledge about the spin interactions of black hole systems. In this work we use black hole perturbation theory to calculate accurately the gravitational waves emanating from the end of the plunging stage of an extreme mass ratio merger in order to further understand this phenomenon. This study focuses primarily on spin induced effects with emphasis on the maximally spinning limit and the identification of possible causes of generic behavior.
We find that gravitational waves emitted during the plunging phase exhibit damped oscillatory behavior, corresponding to a coherent excitation of quasi-normal modes by the test particle. This feature is universal in the sense that the frequencies and damping time do not depend on the orbital parameters of the plunging particle. Furthermore, the observed frequencies are distinct from those associated with the usual free quasi-normal ringing. Our calculation suggests that a maximum in radiated energy and momentum occurs at spin parameters equal to $a/M=0.86$ and $a/M=0.81$, respectively for the plunge stage of a polar orbit. The dependence of linear momentum emission on the angle at which a polar orbit impacts the horizon is quantified. One of the advantages of the perturbation approach adopted here is that insight into the actual mechanism of radiation emission and its relationship to black hole ringing is obtained by carefully identifying the dominant terms in the expansions used.
We calculate the self force acting on a scalar particle which is falling radially into a Schwarzschild black hole. We treat the particle's self-field as a linear perturbation over the fixed Schwarzschild background. The force is calculated by numerically solving the appropriate wave equation for each mode of the field in the time domain, calculating its contribution to the self force, and summing over all modes using Ori's mode-sum regularization prescription. The radial component of the force is attractive at large distances, and becomes repulsive as the particle approaches the event horizon.
Electromagnetic radiation emitted by a charged particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole is examined. Both even- and odd-parity electromagnetic perturbations are considered. They are described by using gauge invariant master functions and the regularized multipolar waveforms as well as their unregularized counterparts constructed from the quasinormal-mode spectrum are obtained for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle. They are in excellent agreement and the resu…
X-ray reflection spectroscopy is a powerful tool to probe the strong gravity region around black holes, but the available relativistic reflection models have a number of simplifications that lead to systematic uncertainties (not fully under control) in the measurement of the properties of a source. In Paper I, we considered the case of an optically thin plunging region and we studied the impact of the radiation produced by the other side of the disk or circling the black hole one or more times. In the present paper, we discuss the case of an optically thick plunging region and we study the imp…
We compute the gravitational self-force (or ``radiation reaction'' force) acting on a particle falling radially into a Schwarzschild black hole. Our calculation is based on the ``mode-sum'' method, in which one first calculates the individual $\ell$-multipole contributions to the self-force (by numerically integrating the decoupled perturbation equations) and then regularizes the sum over modes by applying a certain analytic procedure. We demonstrate the equivalence of this method with the $ζ-$function scheme. The convergence rate of the mode-sum series is considerably improved here (thus nota…
With the possibility of testing massive gravity in the context of black hole physics in mind, we consider the radiation produced by a particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. In order to circumvent the difficulties associated with black hole perturbation theory in massive gravity, we use a toy model in which we replace the graviton field with a massive scalar field and consider a linear coupling between the particle and this field. We compute the waveform generated by the plunging particle and study its spectral content. This pe…
Gravitational waves in massive gravity: Waveforms generated by a particle plunging into a black hole and the excitation of quasinormal modes and quasibound states
We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a sp…
We argue that a genuine image of the black hole viewed by a distant observer is not its shadow, but a more compact event horizon image probed by the luminous matter plunging into black hole. The external border of the black hole shadow is washed out by radiation from matter plunging into black hole and approaching the event horizon. This effect will crucially influence the results of future observations by the Event Horizon Telescope. We show that gravitational lensing of the luminous matter plunging into black hole provides the possibility for visualization of the event horizon. The lensed im…
There are many simplifications in current relativistic reflection models and this introduces systematic uncertainties in the measurement of the properties of the source. In this paper, we study the impact of the radiation crossing the equatorial plane between the black hole and the inner edge of the accretion disk; that is, the radiation produced by the other side of the disk or circling the black hole one or more times (higher order disk images). For slow-rotating black holes with a larger plunging region, the effect is not very sensitive to the exact inclination angle of the disk. For fast-r…
We discuss a new ringdown frequency mode for vacuum perturbations of the Kerr black hole. We evolve initial data for the vacuum radial Teukolsky equation using a near horizon approximation, and find a frequency mode analogous to that found in a recent study of radiation generated by a plunging particle close to the Kerr horizon. We discuss our results in the context of that study. We also explore the utility of this mode by fitting a numerical waveform with a combination of the usual quasi-normal modes (QNMs) and the new oscillation frequency.
We consider the equation of motion of a charged particle or a charged compact object in curved space-time, under the reaction of electromagnetic radiation and also consider a physical situation such that the charged particle or compact object emits gravitational radiation, thereby gravitational radiation reaction also acts on it. We investigate the effect of this metric perturbation i.e. the gravitational radiation on the electromagnetic self-force. We show that, besides the interaction terms derived by P. Zimmerman and E. Poisson (Phys. Rev. D 90, 084030, 2014), additional perturbative terms …
Black hole candidates in X-ray binary systems and at the centers of galaxies are expected to be the Kerr black holes of General Relativity, but the actual nature of these objects has yet to be verified. In this paper, we consider the possibility that they are exotic compact objects and we describe their exterior gravitational field with a subclass of the Manko-Novikov metrics, which are exact solutions of the vacuum Einstein's equations and can describe the spacetime geometry around bodies with arbitrary mass-multipole moments. We point out that around a Manko-Novikov object there may exist ma…
We study the gravitational radiation emitted by a massive point particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. We consider both even- and odd-parity perturbations and describe them using the two gauge-invariant master functions of Cunningham, Price, and Moncrief. We obtain, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over of a large number of modes, and their unregularized counterparts co…
A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.
Ultrarelativistic collisions of black holes are ideal gedanken experiments to study the nonlinearities of general relativity. In this paper we use semianalytical tools to better understand the nature of these collisions and the emitted gravitational radiation. We explain many features of the energy spectra extracted from numerical relativity simulations using two complementary semianalytical calculations. In the first calculation we estimate the radiation by a "zero-frequency limit" analysis of the collision of two point particles with finite impact parameter. In the second calculation we repl…
Hawking's seminal discovery of black hole evaporation was based on the semi-classical, perturbative method. Whether black hole evaporation may result in the loss of information remains undetermined. The solution to this paradox would most likely rely on the knowledge of the end-life of the evaporation, which evidently must be in the non-perturbative regime. Here we reinterpret the Hawking radiation as the tunneling of instantons, which is inherently non-perturbative. For definitiveness, we invoke the picture of shell-anti-shell pair production and show that it is equivalent to that of instanto…
Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and smearing the singularities in the particle source term by the use of narrow Gaussian distributions, we have been able to reproduce earlier results for equatorial circular orbits that were computed using the frequency domain formalism. A time domain prescription for a more general evolution of nearly geodesic orbits under the effects of radiation reaction is presented. This approach can be useful when tackling the more realistic problem of a stellar-mass black hole moving on a generic orbit around a supermassive black hol…
The conformally flat families of initial data typically used in numerical relativity to represent boosted black holes are not those of a boosted slice of the Schwarzschild spacetime. If such data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to ``boosted Schwarzschild'' form. We attempt to compute this radiation by treating the geometry for a single boosted conformally flat hole as a perturbation of a Schwarzschild black hole, which requires the use of second order perturbation theory. In this we attempt t…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is here analyzed by studying the corresponding second-order hyperbolic operator with variable coefficients, instead of using the reduction method from the retarded flat-space Green function in four dimensions. After r…
There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking's original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the end-stage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. W…
In a recent paper we showed that for eccentric-orbit extreme-mass-ratio inspirals the analytic forms of the leading-logarithm energy and angular momentum post-Newtonian (PN) flux terms (radiated to infinity) can, to arbitrary PN order, be determined by sums over the Fourier spectrum of the Newtonian quadrupole moment. We further showed that an essential part of the eccentricity dependence of the related subleading-logarithm PN sequences, at lowest order in the symmetric mass ratio $ν$, stems as well from the Newtonian quadrupole moment. Once that part is factored out, the remaining eccentricit…
We present a generally applicable formalism for modeling the emission, absorption, reflection, and reprocessing of radiation by moving plasma streams close to a Kerr Black hole. The formalism can be used to investigate the observational signatures of a wide range of phenomena, including: (i) the reflection of coronal X-ray radiation off plasma plunging from the inner edge of a black hole accretion disk towards the black hole; (ii) the reflection of coronal X-ray emission off the upper layers of a geometrically thick accretion flow; (iii) the illumination of the accretion disk by a corona movin…
Here we present the results of applying the generalized Riemann zeta-function regularization method to the gravitational radiation reaction problem. We analyze in detail the headon collision of two nonspinning black holes with extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.
Under the dissipative effects of gravitational radiation, black hole binaries will transition from an inspiral to a plunge. The separatrix between bound and plunging orbits features prominently in the transition. For equatorial Kerr orbits, we show that the separatrix is a homoclinic orbit in one-to-one correspondence with an energetically-bound, unstable circular orbit. After providing a definition of homoclinic orbits, we exploit their correspondence with circular orbits and derive exact solutions for them. This paper focuses on homoclinic behavior in physical space, while in a companion pap…
Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the electric and magnetic parts of the Weyl curvature tensor, form the basis of a recently developed approach to visualizing spacetime curvature. In particular, this method has been proposed as a tool for interpreting results from numerical binary black hole simulations, providing a deeper insight into the physical processes governing the merger of black holes and the emission of gravitational radiation. Here we apply this approach to approximate but analytical initial data for both single boosted and binary black holes. …
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to pro…
The decay widths of the quantum black hole precursors, determined from the poles of the resummed graviton propagator, are matched to the expected lifetime given by the Hawking decay. In this way, we impose a sort of duality between a perturbative description and an essentially non-perturbative description, bearing some similarity with the Bloom-Gilman duality for the strong interactions. General relations are then obtained for the widths and masses of the poles in terms of the number of particle species and the renormalisation scale of gravity.
We compute the energy spectra of the gravitational signals emitted when a pointlike mass moves on a closed orbit around a non rotating neutron star, inducing a perturbation of its gravitational field and its internal structure. The Einstein equations and the hydrodynamical equations are perturbed and numerically integrated in the frequency domain. The results are compared with the energy spectra computed by the quadrupole formalism which assumes that both masses are pointlike, and accounts only for the radiation emitted because the orbital motion produces a time dependent quadrupole moment. Th…
We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and 3D distorted black hole spacetimes. In 2D, waveforms for different modes of the radiation are presented, comparing full nonlinear evolutions for different axisymmetric l-modes with perturbative evolutions. We show how axisymmetric black hole codes solving the full, nonlinear Einstein equations are capable of very accurate evolutions, and also how these techni…
We construct Faddeev-Kulish states in QED and perturbative quantum gravity to subleading order in the soft momentum expansion and to first order in the coupling constant, using the charge conservation formula of asymptotic symmetries associated with the tree-level subleading soft theorems. We demonstrate that the emission and absorption of soft photons/gravitons in dressed amplitudes vanish. The fact that no additional soft radiation may be added to a dressed amplitude supports the claim that, in the dressed state formalism, the soft and hard sectors of scattering processes are correlated. We …
We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal choice of the mesh refinement (plus large computational resources). We achieve a convergent set of results for simulations starting with a small nonspinning black hole just outside the ISCO that then performs over two orbits before plunging into the 100 times more massive black hole. We compute the gravitational energy and momenta radiated as well as the fi…
We present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q = M_1/M_2 = {1,0.85,0.78,0.55,0.32}, or equivalently, with reduced mass parameters $η=M_1M_2/(M_1+M_2)^2 = {0.25, 0.248, 0.246, 0.229, 0.183}$. For each case, the initial binary orbital parameters are chosen from the Cook-Baumgarte equal-mass ISCO configuration. We show waveforms of the dominant l=2,3 modes and compute estimates of energy and angular momentum radiated. For the plunges from the close separations…
We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.…
Black hole perturbation theory for Kerr black holes is best studied in the Newman Penrose Formalism, in which gravitational waves are described as perturbations in the Weyl scalars $ψ_0$ and $ψ_4$, with the governing equation being the well-known Teukolsky equation. Near infinity and near horizon, $ψ_4$ is dominated by the component that corresponds to waves propagating towards the positive radial direction, while $ψ_0$ is dominated by the component that corresponds to waves that propagate towards the negative radial direction. Since gravitational-wave detectors measure out-going waves at infi…
We present a pedagogical introduction to the problem of evolving a head on collision of two Aichelburg-Sexl gravitational shock waves in D-dimensions, using perturbative techniques. We follow a constructive approach with examples, going in some detail through: the set up of the exact initial conditions and their properties; perturbative methods in flat space-time with Green function solutions; and numerical strategies to evaluate the integral solutions. We also discuss, briefly, radiation extraction methods adapted to this problem, together with some of the results for this system.
Recent general relativistic magneto-hydrodynamic (MHD) simulations of accretion onto black holes have shown that, contrary to the basic assumptions of the Novikov-Thorne model, there can be substantial magnetic stress throughout the plunging region. Additional dissipation and radiation can therefore be expected. We use data from a particularly well-resolved simulation of accretion onto a non-spinning black hole to compute both the radiative efficiency of such a flow and its spectrum if all emitted light is radiated with a thermal spectrum whose temperature matches the local effective temperatu…
Perturbative dynamics of gravity is investigated for high energy scattering and in black hole backgrounds. In the latter case, a straightforward perturbative analysis fails, in a close parallel to the failure of the former when the impact parameter reaches the Schwarzschild radius. This suggests a flaw in a semiclassical description of physics on spatial slices that intersect both outgoing Hawking radiation and matter that has carried information into a black hole; such slices are instrumental in a general argument for black hole information loss. This indicates a possible role for the proposa…
We establish a correspondence between perturbative classical gluon and gravitational radiation emitted by spinning sources, to linear order in spin. This is an extension of the non-spinning classical perturbative double copy and uses the same color-to-kinematic replacements. The gravitational theory has a scalar (dilaton) and a 2-form field (the Kalb-Ramon axion) in addition to the graviton. In arXiv:1712.09250, we computed axion radiation in the gravitational theory to show that the correspondence fixes its action. Here, we present complete details of the gravitational computation. In particu…
Moduli fields generically produce strong dark matter -- radiation and baryon -- radiation isocurvature perturbations through their decay if they remain light during inflation. We show that existing upper bounds on the magnitude of such fluctuations can thus be translated into stringent constraints on the moduli parameter space m_σ(modulus mass) -- σ_{inf} (modulus vacuum expectation value at the end of inflation). These constraints are complementary to previously existing bounds so that the moduli problem becomes worse at the perturbative level. In particular, if the inflationary scale H_{inf}…
The physical observables of quantum theory can be described by perturbation theory, which is often given by diverging power series. This divergence is connected to the existence of non-perturbative phenomena, where resurgence allows us to study this connection. Applying this idea to the WKB expansion, the exact WKB analysis gives a clear connection to non-perturbative phenomena. In this paper, we apply the exact WKB analysis to the Unruh effect and Hawking radiation. The mechanism we found in this paper is similar to the Schwinger effect of a constant electric field, where the background is st…
Exact Cancellation of Horizon Modes in Kerr Ringdown
Institute for Cosmic Ray Research, The University of Tokyo（宇宙射线研究所，东京大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理系）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（宇宙早期研究中心（RESCEU），东京大学理学研究科）
We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits…
We undertake a hydrodynamical study of a mixture of tightly coupled primordial radiation, neutrinos, baryons, electrons and positrons, together with a gas of already decoupled dark matter WIMPS and an already existing "frozen" magnetic field in the infinite conductivity regime. Considering this cosmic fluid as the source of a homogeneous but anisotropic Bianchi I model, we describe its interaction with the magnetic field by means of suitable equations of state that are appropriate for the particle species of the mixture between the end of the leptonic era and the beginning of the radiation-dom…
We have studied the main features of the gravitational radiation generated by an astrophysical system constituted of three compact objects attracting one another (only via gravitational interaction) in such a manner that stable orbits do exist. We have limited our analysis to systems that can be treated with perturbative methods. We show the profile of the gravitational waves emitted by such systems. These results can be useful within the framework of the new gravitational astronomy which will be made feasible by means of the new generation of gravitational detectors such as LISA in a no longe…
