The absorption cross section of rotating black holes in the Randall-Sundrum brane-world scenario for massless scalar waves is obtained via the partial-wave method. A variety of incidence directions with respect to the black hole rotation axis is considered. Special attention is given to near-extreme black holes, in which cases the absorption cross section increases as the tidal charge becomes more negative. It is shown that black holes with different configurations can present capture cross sections/shadows of same size. However, in such cases, the absorption spectra are different mainly for small frequencies. Numeric results are compared with the capture cross sections in the high-frequency limit, and with the black hole area in the low-frequency limit showing good agreement.
The changes a (negative) tidal charge causes at the phenomenon of superradiance which occurs around rotating black holes are investigated. This is made by computing the amplification factors of massless scalar waves being scattered by the black hole. It is shown that the increase of the tidal charge intensity leads to a considerable enhancement of energy extraction from near-extreme black holes. Such improvement results from the fact that extreme black holes with more negative tidal charges spin faster. Maximum amplification decreases with the increase of the tidal charge intensity if the angu…
We construct the external metric of a slowly rotating, tidally deformed material body in general relativity. The tidal forces acting on the body are assumed to be weak and to vary slowly with time, and the metric is obtained as a perturbation of a background metric that describes the external geometry of an isolated, slowly rotating body. The tidal environment is generic and characterized by two symmetric-tracefree tidal moments E_{ab} and B_{ab}, and the body is characterized by its mass M, its radius R, and a dimensionless angular-momentum vector χ^a << 1. The perturbation accounts for all c…
The metric outside a compact body deformed by a quadrupolar tidal field is universal up to its Love numbers, constants which encode the tidal response's dependence on the body's internal structure. For a non-rotating body, the deformed external geometry is characterized by the familiar gravitational Love numbers $K_2^{\text{el}}$ and $K_2^{\text{mag}}$. For a slowly rotating body, these must be supplemented by rotational-tidal Love numbers, which measure the response to couplings between the body's spin and the external tidal field. By integrating the interior field equations, I find that the …
It was recently revealed that a rotating compact body responds dynamically when it is subjected to a gravitomagnetic tidal field, even when this field is idealized as time-independent. The dynamical response is characterized by time-changing internal currents, and it was suspected to originate from zero-frequency g-modes and r-modes driven by the tidal forces. In this paper we provide additional insights into the phenomenon by examining the tidal response of a rotating body within the framework of post-Newtonian gravity. This approach allows us to develop an intuitive picture for the phenomeno…
Tidal indicators are commonly associated with the electric and magnetic parts of the Riemann tensor (and its covariant derivatives) with respect to a given family of observers in a given spacetime. Recently, observer-dependent tidal effects have been extensively investigated with respect to a variety of special observers in the equatorial plane of the Kerr spacetime. This analysis is extended here by considering a more general background solution to include the case of matter which is also endowed with an arbitrary mass quadrupole moment. Relation with curvature invariants and Bel-Robinson ten…
The effects of the tidal charge of black holes predicted in the Randall-Sundrum brane-world scenario on the electromagnetic cross sections and emission rate is studied. Although quantitatively different, the cross sections and emission rates of such black holes are similar to the ones of Schwarzschild black holes. The increase of the tidal-charge intensity makes the absorption cross sections increase and the interference-fringe widths of the differential scattering cross sections narrow. The electromagnetic emission rate increases initially with the increase of the tidal-charge intensity, but …
In rotating viscous fluid stars, tidal torque leads to an exchange of spin and orbital angular momentum. The horizon of a black hole has an effective viscosity that is large compared to that of stellar fluids, and an effective tidal torque may lead to important effects in the strong field interaction at the endpoint of the inspiral of two rapidly rotating holes. In the most interesting case both holes are maximally rotating and all angular momenta (orbital and spins) are aligned. We point out here that in such a case (i) the transfer of angular momentum may have an important effect in modifyin…
We investigate the shadow cast by a rotating braneworld black hole, in the Randall-Sundrum scenario. In addition to the angular momentum, the tidal charge term deforms the shape of the shadow. For a given value of the rotation parameter, the presence of a negative tidal charge enlarges the shadow and reduces its deformation with respect to Kerr spacetime, while for a positive charge, the opposite effect is obtained. We also analyze the case in which the combination of the rotation parameter and the tidal charge results in a naked singularity. We discuss the observational prospects correspondin…
In the first part of this article I determine the geometry of a slowly rotating black hole deformed by generic tidal forces created by a remote distribution of matter. The metric of the deformed black hole is obtained by integrating the Einstein field equations in a vacuum region of spacetime bounded by r < r_max, with r_max a maximum radius taken to be much smaller than the distance to the remote matter. The tidal forces are assumed to be weak and to vary slowly in time, and the metric is expressed in terms of generic tidal quadrupole moments E_{ab} and B_{ab} that characterize the tidal envi…
We compute numerically the absorption cross section of planar massless scalar waves impinging upon a Kerr-Newman black hole with different incidence angles. We investigate the influence of the black hole electric charge and angular momentum in the absorption spectrum, comparing our numerical computations with analytical results for the limits of high and low frequency.
Perturbations in a draining vortex can be described analytically in terms of confluent Heun functions. In the context of analogue models of gravity in ideal fluids, we investigate analytically the absorption length of waves in a draining bathtub, a rotating black hole analogue, using confluent Heun functions. We compare our analytical results with the corresponding numerical ones, obtaining excellent agreement.
We analytically study the scalar perturbation of non-asymptotically flat (NAF) rotating linear dilaton black holes (RLDBHs) in 4-dimensions. We show that both radial and angular wave equations can be solved in terms of the hypergeometric functions. The exact greybody factor (GF), the absorption cross-section (ACS), and the decay rate (DR) for the massless scalar waves are computed for these black holes (BHs). The results obtained for ACS and DR are discussed through graphs.
We study the absorption of monochromatic electromagnetic plane waves impinging upon a Kerr black hole, in the general case that the direction of incidence is not aligned with the black hole spin axis. We present numerical results that are in accord with low- and high-frequency approximations. We find that circularly-polarized waves are distinguished by the black hole spin, with counter-rotating polarizations being more absorbed than co-rotating polarizations. At low frequencies and moderate incidence angles, there exists a narrow parameter window in which superradiant emission in the dipole mo…
The gravitomagnetic tidal Love number of a slowly rotating body was calculated previously under the assumption that the velocity perturbation created by the tidal field consists of an induction piece proportional to the vector potential, and a rotational piece that scales with $Ω$, the body's angular velocity. The second part of this assumption is wrong: the rotational piece of the velocity perturbation scales in fact like $Ω^0 = 1$. The previous calculations are therefore incorrect, and the purpose of this paper is to repair the mistake. To keep the technical difficulties to a minimum, the tr…
In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are re…
For a test particle approaching a rapidly rotating black hole we find a range of values of the particle's energy and angular momentum, on the order of 1\% or more of the corresponding values of the hole, such that three conditions are satisfied. 1) The particle can reach the horizon. 2) After absorption the new hole still has a horizon. 3) The area of the new hole is less than the area of the original one, in apparent violation of a theorem of Hawking. We offer support for the claim that the test particle approximation is the cause of the violation.
When a particle moves around a Kerr black hole, it radiates gravitational waves.Some of these waves are absorbed by the black hole. We calculate such absorption of gravitational waves induced by a particle of mass mu in a circular orbit on an equatorial plane around a Kerr black hole of mass M. We assume that the velocity of the particle v is much smaller than the speed of light c and calculate the energy absorption rate analytically. We adopt an analytic technique for the Teukolsky equation developed by Mano, Suzuki and Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to …
We propose an approximate approach for studying the relativistic regime of stellar tidal disruptions by rotating massive black holes. It combines an exact relativistic description of the hydrodynamical evolution of a test fluid in a fixed curved spacetime with a Newtonian treatment of the fluid's self-gravity. Explicit expressions for the equations of motion are derived for Kerr spacetime using two different coordinate systems. We implement the new methodology within an existing Newtonian Smoothed Particle Hydrodynamics code and show that including the additional physics involves very little e…
Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Graduate School of Science, The University of Tokyo（东京大学理学研究科）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学宇宙物质量子前沿研究中心（WPI），东京大学高等研究院，东京大学）；The Hakubi Center for Advanced Research, Kyoto University（京都大学博慧中心）；RIKEN iTHEMS（理化学研究所 iTHEMS）；Department of Physics, College of Humanities and Sciences, Nihon University（日本大学文理学部物理学系）；High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University（朱拉隆功大学理学院物理学系高能物理研究组）
A binary system composed of an oscillating and rotating coplanar dusty disk and a point mass is considered. The conservative dynamics is treated on the Newtonian level. The effects of gravitational radiation reaction and wave emission are studied to leading quadrupole order. The related waveforms are given. The dynamical evolution of the system is determined semi-analytically exploiting the Hamiltonian equations of motion which comprise the effects both of the Newtonian tidal interaction and the radiation reaction on the motion of the binary system in elliptic orbits. Tidal resonance effects b…
It is shown analytically that an external tidal gravitational field increases the secular stability of a fully general relativistic, rigidly rotating neutron star that is near marginal stability, protecting it against gravitational collapse. This stabilization is shown to result from the simple fact that the energy $δM(Q,R)$ required to raise a tide on such a star, divided by the square of the tide's quadrupole moment $Q$, is a decreasing function of the star's radius $R$, $(d/dR)[δM(Q,R)/Q^2]<0$ (where, as $R$ changes, the star's structure is changed in accord with the star's fundamental mode…
Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the binary's members, changing them (at lowest order) from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian gravity, there are simple connections between the geometry of the distorted ellipsoid and the impact of tides on the orbit's evolution. In this paper, we develop tools for investigating tidal distortions of rapidly rotating black holes using techniques that are good for strong-field, fast-moti…
We study the innermost stable circular orbit (ISCO) of a spinning test particle moving in the vicinity of an axially symmetric rotating braneworld black hole (BH). We start with the description of the event horizon, static limit surface and ergosphere region of such BH and bring out the effect of tidal charge parameter on ergosphere. It is found that the ISCO of rotating braneworld BH is very sensitive to braneworld BH parameter C (also known as tidal charge parameter) in addition to its rotation parameter. We further discovered that the orbital radius of the spinning test particles changes no…
Observations of gravitational waves from inspiralling neutron star binaries---such as GW170817---can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called "Love numbers." The tidal Love numbers $k_2^\text{el}$ and $k_2^\text{mag}$ measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers $\mathfrak{f}^\text{o}$ and $\…
The first objective of this work is to obtain practical prescriptions to calculate the absorption of mass and angular momentum by a black hole when external processes produce gravitational radiation. These prescriptions are formulated in the time domain within the framework of black-hole perturbation theory. Two such prescriptions are presented. The first is based on the Teukolsky equation and it applies to general (rotating) black holes. The second is based on the Regge-Wheeler and Zerilli equations and it applies to nonrotating black holes. The second objective of this work is to apply the t…
We show that rotating black holes do not experience any tidal deformation when they are perturbed by a weak and adiabatic gravitational field. The tidal deformability of an object is quantified by the so-called "Love numbers", which describe the object's linear response to its external tidal field. In this work, we compute the Love numbers of Kerr black holes and find that they vanish identically. We also compute the dissipative part of the black hole's tidal response, which is non-vanishing due to the absorptive nature of the event horizon. Our results hold for arbitrary values of black hole …
In previous work, we developed tools for quantifying the tidal distortion of a black hole's event horizon due to an orbiting companion. These tools use techniques which require large mass ratios (companion mass $μ$ much smaller than black hole mass $M$), but can be used for arbitrary bound orbits, and for any black hole spin. We also showed how to visualize these distorted black holes by embedding their horizons in a global Euclidean 3-space, ${\mathbb{E}}^3$. Such visualizations illustrate interesting and important information about horizon dynamics. Unfortunately, we could not visualize blac…
In a previous paper, we developed tools for studying the horizon geometry of a Kerr black hole that is tidally distorted by a binary companion using techniques that require large mass ratios but can be applied to any bound orbit and allow for arbitrary black hole spin. We now apply these tools to generic Kerr black hole orbits. This allows us to investigate horizon dynamics: the tidal field perturbing the horizon's geometry varies over a generic orbit, with significant variations for eccentric orbits. Many of the features of the horizon's behavior found previously carry over to the dynamical c…
We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness…
Moment of inertia ($I$), rotational~(tidal) Love number ($λ^{\rm (rot)}$) and quadrupole moment ($Q$) of slowly rotating massive neutron star~(NS) with holographic multiquark~(MQ) core are computed in comparison to pure MQ star. The Chiral Effective Theory~(CET) stiff equation of state~(EoS) is used in the crust of the neutron star. The dimensionless multipole moments $\bar{I},\barλ^{\rm (rot)}, \bar{Q}$ are found to be independent of the rotation parameters and determined completely by the zeroth-order star profile. Universal ``I-Love-Q'' relations found by Yagi and Yunes [1,2] are mostly pre…
In the first part of the paper we construct the metric of a tidally deformed, nonrotating black hole. The metric is presented as an expansion in powers of r/b << 1, in which r is the distance to the black hole and b the characteristic length scale of the tidal field --- the typical distance to the remote bodies responsible for the tidal environment. The metric is expanded through order (r/b)^4 and written in terms of a number of tidal multipole moments, the gravitoelectric moments E_{ab}, E_{abc}, E_{abcd} and the gravitomagnetic moments B_{ab}, B_{abc}, B_{abcd}. It differs from the similar c…
We present the results of relativistic smoothed particle hydrodynamics simulations of tidal disruptions of stars by rotating supermassive black holes, for a wide range of impact parameters and black hole spins. For deep encounters, we find that: relativistic precession creates debris geometries impossible to obtain with the Newtonian equations; part of the fluid can be launched on plunging orbits, reducing the fallback rate and the mass of the resulting accretion disc; multiple squeezings and bounces at periapsis may generate distinctive X-ray signatures resulting from the associated shock bre…
In this article, we study the shadow produced by rotating black holes with a tidal charge in a Randall-Sundrum braneworld model, with a cosmological constant. We obtain the apparent shape and the corresponding observables for different values of the tidal charge and the rotation parameter, and we analyze the influence of the presence of the cosmological constant. We also discuss the observational prospects for this optical effect.
We study exact stationary and axisymmetric solutions describing charged rotating black holes localized on a 3-brane in the Randall-Sundrum braneworld. The charges of the black holes are considered to be of two types, the first being an induced tidal charge that appears as an imprint of nonlocal gravitational effects from the bulk space and the second is a usual electric charge arising due to a Maxwell field trapped on the brane. We assume a special ansatz for the metric on the brane taking it to be of the Kerr-Schild form and show that the Kerr-Newman solution of ordinary general relativity in…
Spin the black circle II: tidal heating and torquing of a rotating black hole by a test mass on generic orbits
University of California, Berkeley（加州大学伯克利分校）；The Pennsylvania State University（宾夕法尼亚州立大学）；Universitá degli Studi di Torino（都灵大学）；INFN sezione di Torino（意大利国家核物理研究所都灵分部）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）
The effect of energy absorption during the binary evolution of Exotic-compact-objects (ECOs) is extensively studied. We review the underlying mechanism that provides the energy dissipation in material objects - tidal friction. We show that unlike typical astrophysical objects, where absorption due to viscosity is negligible, in ECOs, absorption could potentially mimic the analogous effect of black-holes (BHs) - tidal heating. We stand for their differences and similarities in the context of energy dissipation during the inspiral. Inspired by the membrane paradigm and recent studies, we demonst…
We analyse the superradiant stability of braneworld extremal Kerr and Kerr-Newman black holes under massive scalar perturbation. These black hole solutions differ from their four dimensional counterpart by the presence of a tidal charge, which unlike electric charge, can take both positive and negative values and carries the signature of extra dimensions. We consider the perturbation of the brane geometry by a massive scalar field. From the radial equation of motion of the scalar field, we have found the effective potential felt by the field. For superradiant stability, there should not be any…
Tidal perturbations and Love Symmetry for five-dimensional charged rotating black holes
University of Pennsylvania（宾夕法尼亚大学）；University of Maribor（马里博尔大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Ivan Franko National University of Lviv（利沃夫伊万·弗兰科国立大学）
Gravitational wave observation has the potential of probing ultralight bosonic fields such as axion. Axion forms a cloud around a rotating black hole (BH) by superradiant instability and should affect the gravitational waveform from binary BHs. On the other hand, considering the cloud associated with a BH in a binary system, tidal interaction depletes the cloud in some cases during the inspiral phase. We made the exhaustive study of cloud depletion numerically in a wide parameter range for equal mass binaries, assuming only the quadrupolar tidal perturbation is at work. We found that clouds ca…
We consider misaligned accretion discs formed after tidal disruption events occurring when a star encounters a supermassive rotating black hole. We use the linear theory of warped accretion discs to find the disc shape when the stream produced by the disrupted star provides a source of mass and angular momentum that is misaligned with the black hole. The evolution of the surface density and aspect ratio is found from a one dimensional vertically averaged model. We extend previous work which assumed a quasi-stationary disc to allow unrestricted dynamical propagation of disc tilt and twist throu…
In this paper we analyze a binary system consisting of a star and a rotating black hole. The electromagnetic radiation emitted by the star interacts with the background of the black hole and stimulates the production of dilaton waves. We then estimate the energy transferred from the electromagnetic radiation of the star to the dilaton field as a function of the frequency. The resulting picture is a testable signature of the existence of dilaton fields as predicted by string theory in an astrophysical context.
In a coalescing neutron star-neutron star (NS-NS) or neutron star-black hole (NS-BH) binary, oscillation modes of the NS can be resonantly excited by the companion during the final minutes of the inspiral. The resonant energy transfer between the orbit and NS speeds up or slows down the inspiral and induces a phase change in the emitted gravitational waves from the binary. A tidal resonance, (jk,m), occurs when the mode frequency equals m times the orbital frequency. For f-mode resonance to occur before coalescence, the NS must have rapid rotation, with spin frequency nu_s>710Hz for (22,2)-res…
Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole
Università di Perugia（佩鲁贾大学）；Niels Bohr Institute, Copenhagen University（哥本哈根大学尼尔斯·玻尔研究所）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
Formulation of the Lagrangian approach is presented for studying features of motions of stellar bodies with non-zero rest mass in the vicinity of fast-spinning black holes. The structure of Lagrangian is discussed. The general method is applied to description of body motion in the Kerr model of space-time to transition to the problem of tidal disruption of elastic bodies by strong gravitational field.
Analytical solutions of Maxwell equations in background spacetime of black hole in braneworld immersed in external uniform magnetic field have been found. Influence of both magnetic and brane parameters on effective potential of the radial motion of charged test particle around slowly rotating black hole in braneworld immersed in uniform magnetic field has been investigated by using Hamilton-Jacobi method. Exact analytical solution for dependence of the radius of the innermost stable circular orbits (ISCO) $r_{\rm ISCO}$ from brane parameter for motion of test particle around nonrotating isola…
The thermodynamics of Myers-Perry black holes in general dimensions are studied using a particle probe. When undergoing particle absorption, the changes of the entropy and irreducible mass are shown to be dependent on the particle radial momentum. The black hole thermodynamic behaviors are dependent on dimensionality for specific rotations. For a 4-dimensional Kerr black hole, its black hole properties are maintained for any particle absorption. 5-dimensional black holes can avoid a naked ring singularity by absorbing a particle in specific momenta ranges. Black holes over 6 dimensions become …
We point out novel consequences of general relativity involving tidal dynamics of ultrarelativistic relative motion. Specifically, we use the generalized Jacobi equation and its extension to study the force-free dynamics of relativistic flows near a massive rotating source. We show that along the rotation axis of the gravitational source, relativistic tidal effects strongly decelerate an initially ultrarelativistic flow with respect to the ambient medium, contrary to Newtonian expectations. Moreover, an initially ultrarelativistic flow perpendicular to the axis of rotation is strongly accelera…
This is a study of the scattering and absorption of planar gravitational waves by a Kerr black hole in vacuum. We apply the partial wave method to compute cross sections for the special case of radiation incident along the rotation axis. A catalogue of numerically-accurate cross sections is presented, for a range of incident wavelengths $Mω\le 4$ and rotation rates $a \le 0.999M$. Three effects are studied in detail: polarization, helicity-reversal and glory scattering. First, a new approximation to the polarization in the long-wavelength limit is derived. We show that black hole rotation dist…
A constraint on the tidal charge generated within a brane world is shown. Using the shadow of a rotating black hole in a brane context in order to describe the M87* parameters recently announced by the Event Horizon Telescope Collaboration, the deviation from circularity of the reported shadow produces an upper bound on the bulk's nonlocal effect, which is conceived of as a tidal charge in the four-dimensional brane induced by the five-dimensional bulk. Therefore, a deviation from circularity $\lesssim 10\%$ leads to an upper bound on the tidal charge $\lesssim 0.004M^2$.
