The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics, astrophysics and gravitational-wave astronomy. Love tensors characterize the tidal deformability of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation. In contrast to this result, we show that Love tensors are generically nonzero for a spinning black hole. Specifically, to linear order in the Kerr black hole spin and the weak perturbing tidal field, we compute in closed form the Love tensors that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields. For a dimensionless spin ~ 0.1, the nonvanishing quadrupolar Love tensors are ~ 0.002, thus showing that black holes are particularly "rigid" compact objects.
The coupling between the angular momentum of a compact object and an external tidal field gives rise to the "rotational" tidal Love numbers, which affect the tidal deformability of a spinning self-gravitating body and enter the gravitational waveform of a binary inspiral at high post-Newtonian order. We provide numerical evidence for a surprising "hidden" symmetry among the rotational tidal Love numbers with opposite parities, which are associated to perturbations belonging to separate sectors. This symmetry, whose existence had been suggested on the basis of a Lagrangian description of the ti…
By extending our recent framework to describe the tidal deformations of a spinning compact object, we compute for the first time the tidal Love numbers of a spinning neutron star to linear order in the angular momentum. The spin of the object introduces couplings between electric and magnetic distortions and new classes of spin-induced ("rotational") tidal Love numbers emerge. We focus on stationary tidal fields, which induce axisymmetric perturbations. We present the perturbation equations for both electric-led and magnetic-led rotational Love numbers for generic multipoles and explicitly sol…
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $ψ_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $\ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanis…
The deformability of a compact object induced by a perturbing tidal field is encoded in the tidal Love numbers, which depend sensibly on the object's internal structure. These numbers are known only for static, spherically-symmetric objects. As a first step to compute the tidal Love numbers of a spinning compact star, here we extend powerful perturbative techniques to compute the exterior geometry of a spinning object distorted by an axisymmetric tidal field to second order in the angular momentum. The spin of the object introduces couplings between electric and magnetic deformations and new c…
We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory (EFT) and in general relativity (GR). We point out that the GR amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational non-linearities in the wave region, whose proper treatment requires higher order EFT loop calculations. In particular, the elastic scattering in the near field approximation …
We present a method to construct conformally curved initial data for charged black hole binaries with spin on arbitrary orbits. We generalize the superposed Kerr-Schild, extended conformal thin sandwich construction from [Lovelace et al., Phys. Rev. D {78}, 084017 (2008)] to use Kerr-Newman metrics for the superposed black holes and to solve the electromagnetic constraint equations. We implement the construction in the pseudospectral code SGRID. The code thus provides a complementary and completely independent excision-based construction, compared to the existing charged black hole initial dat…
It was shown recently that the static tidal response coefficients, called Love numbers, vanish identically for Kerr black holes in four dimensions. In this work, we confirm this result and extend it to the case of spin-0 and spin-1 perturbations. We compute the static response of Kerr black holes to scalar, electromagnetic, and gravitational fields at all orders in black hole spin. We use the unambiguous and gauge-invariant definition of Love numbers and their spin-0 and spin-1 analogs as Wilson coefficients of the point particle effective field theory. This definition also allows one to clear…
We construct models of slowly rotating, perfect-fluid neutron stars by extending the classical Hartle-Thorne formalism to generic scalar-tensor theories of gravity. Working at second order in the dimensionless angular momentum, we compute the mass M, radius R, scalar charge q, moment of inertia I and spin-induced quadrupole moment Q, as well as the tidal and rotational Love numbers. Our formalism applies to generic scalar-tensor theories, but we focus in particular on theories that allow for spontaneous scalarization. It was recently discovered that the moment of inertia, quadrupole moment and…
We investigate the merger of a neutron star (of compaction ratio $0.1$) in orbit about a spinning black hole in full general relativity with a mass ratio of $5:1$, allowing for the star to have an initial magnetization of $10^{12} {\rm Gauss}$. We present the resulting gravitational waveform and analyze the fallback accretion as the star is disrupted. The evolutions suggest no significant effects from the initial magnetization. We find that only a negligible amount of matter becomes unbound; $99%$ of the neutron star material has a fallback time of 10 seconds or shorter to reach the region of …
The Mathisson-Papapetrou equations are used for investigations of influence of the spin-gravity coupling on a highly relativistic spinning particle in Schwarzschild's field. It is established that interaction of the particle spin with the gravitomagnetic components of the field, estimated in the proper frame of the particle, causes the large acceleration of the spinning particle relative to geodesic free fall. As a result the accelerated charged spinning particle can generate intensive electromagnetic radiation when its velocity is highly relativistic. The significant contribution of the highl…
Matching Tidal Deformability (Wilson) Coefficients to Black Hole Love Numbers in Higher-Curvature Gravity
Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）；University of Waterloo（滑铁卢大学）；UNESP - Universidade Estadual Paulista（圣保罗州立大学）；King’s College London（伦敦国王学院）；ICTP South American Institute for Fundamental Research（国际理论物理研究所南美基础研究所）
We estimate the accuracy in the measurement of the tidal Love number of a supermassive compact object through the detection of an extreme mass ratio inspiral~(EMRI) by the future LISA mission. A nonzero Love number would be a smoking gun for departures from the classical black hole prediction of General Relativity. We find that an EMRI detection by LISA could set constraints on the tidal Love number of a spinning central object with dimensionless spin $\hat a=0.9$ ($\hat a=0.99$) which are approximately four (six) orders of magnitude more stringent than what achievable with current ground-base…
The multipole moments and the tidal Love numbers of neutron stars and quark stars satisfy certain relations which are almost insensitive to the star's internal structure. A natural question is whether the same relations hold for different compact objects and how they possibly approach the black-hole limit. Here we consider "gravastars", which are hypothetical compact objects sustained by their internal vacuum energy. Such solutions have been proposed as exotic alternatives to the black-hole paradigm because they can be as compact as black holes and exist in any mass range. By constructing slow…
For a large class of space and time-dependent warped geometries we find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in the presence of p-form matter fields. This is done under two conditions on the matter sector which we show impose the integrability of the full system. Solutions are classified and known black hole limits are found. It is shown that Lovelock gravity restricts drastically the possible horizon geometries and allowed matter sources. In fact, we show that if we allow only for solutions of asymptotically flat falloff behaviour, and no fine-tuning of co…
For non-spinning, charged (Reissner-Nordström) black holes, the particles with an opposite sign of charge with respect to that of the black hole will be pulled into the black hole by the extra electromagnetic force. Such a hole will be quickly neutralized so that there should not exist significantly charged, non-spinning black holes in the universe. The case of spinning, charged (Kerr-Newmann) black holes is more complicated. For a given initial position and initial velocity of the particle, an oppositely charged particle does not always more easily fall into the black hole than a neutral part…
We construct conserved quantities in pure Lovelock gravity for both static and dynamic Vaydia-type black holes with AdS, dS and flat asymptotics, applying field-theoretical formalism developed earlier. Global energy (where applicable), quasi-local energy together with fluxes of these quantities are presented for both types of black holes, considering asymptotic spacetime as background. The same quantities are constructed for dynamic black holes on the background of the related static black holes. Besides, for the dynamic black holes, energy densities and densities of energy flux are calculated…
Static electromagnetic Love tensors of 5-dimensional Myers-Perry black holes
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh（爱丁堡大学数学学院与麦克斯韦数学科学研究所）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
It has recently been pointed out that particles falling freely from rest at infinity outside a Kerr black hole can in principle collide with arbitrarily high center of mass energy in the limiting case of maximal black hole spin. Here we aim to elucidate the mechanism for this fascinating result, and to point out its practical limitations, which imply that ultra-energetic collisions cannot occur near black holes in nature.
Ground-based gravitational wave detectors may be able to constrain the nuclear equation of state using the early, low frequency portion of the signal of detected neutron star - neutron star inspirals. In this early adiabatic regime, the influence of a neutron star's internal structure on the phase of the waveform depends only on a single parameter lambda of the star related to its tidal Love number, namely the ratio of the induced quadrupole moment to the perturbing tidal gravitational field. We analyze the information obtainable from gravitational wave frequencies smaller than a cutoff freque…
An important physical phenomenon that manifests itself during the inspiral of two orbiting compact objects is the tidal deformation of each under the gravitational influence of its companion. In the case of binary neutron star mergers, this tidal deformation and the associated Love numbers have been used to probe properties of dense matter and the nuclear equation of state. Non-spinning black holes on the other hand have a vanishing (field) tidal Love number in General Relativity. This pertains to the deformation of the asymptotic gravitational field. In certain cases, especially in the late s…
Gravitational-wave observations in the near future may allow us to measure tidal deformabilities of neutron stars, which leads us to the understanding of physics at nuclear density. In principle, the gravitational waveform depends on various tidal parameters, which correlate strongly. Therefore, it would be useful if one can express such tidal parameters with a single parameter. Here, we report on universal relations among various $\ell$-th (dimensionless) electric, magnetic and shape tidal deformabilities in neutron stars and quark stars that do not depend sensitively on the equation of state…
We present numerical relativity results of tidal disruptions of white dwarfs from ultra-close encounters with a spinning, intermediate mass black hole. These encounters require a full general relativistic treatment of gravity. We show that the disruption process and prompt accretion of the debris strongly depend on the magnitude and orientation of the black hole spin. However, the late-time accretion onto the black hole follows the same decay, $\dot{M}$ ~ t^{-5/3}, estimated from Newtonian gravity disruption studies. We compute the spectrum of the disk formed from the fallback material using a…
We investigate the consequences of throwing point particles into odd-dimensional Myers-Perry black holes in asymptotically anti-de Sitter (AdS) backgrounds. We restrict our attention to the case in which the angular momenta of the background geometry are all equal. This process allows us to test the generalization of the weak cosmic censorship conjecture to asymptotically AdS spacetimes in higher dimensions. We find no evidence for overspinning in D = 5, 7, 9 and 11 dimensions. Instead, test particles carrying the maximum possible angular momentum that still fall into an extremal rotating blac…
Observations of gravitational wave (GW) signals produced by coalescing binary neutron stars (NS), like the GW event GW170817, can be exploited to constrain the equation of state (EoS) of matter in the stars' inner core. The information on the internal structure and composition of the stars is encoded in their tidal Love numbers, which leave an imprint in the waveform of the GW signal emitted from the binary during the late inspiral phase. We extended the theory of tidal deformations of compact objects by computing the spin-tidal corrections that affect the dynamics and the GW emission of a bin…
Dynamical tidal Love numbers of black holes under generic perturbations: Connecting black hole perturbation theory with effective field theory
School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学文化协会物理科学学院）；Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute)（引力物理学马普研究所（爱因斯坦研究所））；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础国际理论科学中心）；Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）
The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green's function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode excitation for Kerr black holes. Relying on the formalism developed by Mano, Suzuki and Takasugi, we improve and extend previous calculations of the quasinormal mode residues in the complex frequency plane ("excitation factors" B_q). Using these results we compute the "excitation coefficients" C_q (essentially the mode amplitudes) in the special case where the s…
We study numerically the late-time tails of linearized fields with any spin $s$ in the background of a spinning black hole. Our code is based on the ingoing Kerr coordinates, which allow us to penetrate through the event horizon. The late time tails are dominated by the mode with the least multipole moment $\ell$ which is consistent with the equatorial symmetry of the initial data and is equal to or greater than the least radiative mode with $s$ and the azimuthal number $m$.
It has recently been pointed out that the spinning Kerr black hole with maximal spin could act as a particle collider with arbitrarily high center-of-mass energy. In this paper, we will extend the result to the charged spinning black hole, the Kerr-Newman black hole. The center-of-mass energy of collision for two uncharged particles falling freely from rest at infinity depends not only on the spin $a$ but also on the charge $Q$ of the black hole. We find that an unlimited center-of-mass energy can be approached with the conditions: (1) the collision takes place at the horizon of an extremal bl…
Relativistic current carrying strings moving axisymmetrically on the background of a Kerr black hole are studied. The boundaries and possible types of motion of a string with a given energy and current are found. Regions of parameters for which the string falls into the black hole, or is trapped in a toroidal volume, or can escape to infinity, are identified, and representative trajectories are examined by numerical integration, illustrating various interesting behaviors. In particular, we find that a string can start out at rest near the equatorial plane and, after bouncing around, be ejected…
Radiative losses from unbound orbits at quadratic order in spin from MPM formalism
Istituto per le Applicazioni del Calcolo “M. Picone,” CNR（意大利国家研究委员会计算应用研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，中国科学院大学）
The recent gravitational wave observations by the LIGO/Virgo collaboration have allowed the first tests of General Relativity in the extreme gravity regime, when comparable-mass black holes and neutron stars collide. Future space-based detectors, such as the Laser Interferometer Space Antenna, will allow tests of Einstein's theory with gravitational waves emitted when a small black hole falls into a supermassive one in an extreme mass-ratio inspiral. One particular test that is tailor-made for such inspirals is the search for chaos in extreme gravity. We here study whether chaos is present in …
We study the transformation of multipolar decompositions of gravitational radiation under rotations and boosts. Rotations to the remnant black hole's frame simplify the waveforms from the merger of generic spinning black hole binaries. Boosts may be important to get an accurate gravitational-wave phasing, especially for configurations leading to large recoil velocities of the remnant. As a test of our formalism we revisit the classic problem of point particles falling into a Schwarzschild black hole. Then we highlight by specific examples the importance of choosing the right frame in numerical…
We investigate the interiors of 3+1 dimensional asymptotically flat charged and rotating black holes as described by observers who fall into the black holes at late times, long after any perturbations of the exterior region have decayed. In the strict limit of late infall times, the initial experiences of such observers are precisely described by the region of the limiting stationary geometry to the past of its inner horizon. However, we argue that late infall-time observers encounter a null shockwave at the location of the would-be outgoing inner horizon. In particular, for spherically symmet…
We study the spacetime noncommutative effect on black hole as particle accelerators and, find that particle falling from infinity with zero velocity cannot collide with unbound energy when the noncommutative Kerr black hole is exactly extremal. Our results also show that the bigger of the spinning black hole's mass is, the higher of center of mass energy that the particles obtain. For small and medium noncommutative Schwarzschild black hole, the collision energy depends on the black holes' mass.
Attempts to find black hole microstates using the Hamiltonian phase space approach have been made on the Schwarzschild spacetime. Since the Schwarzschild spacetime is also in the larger family of the Kerr spacetimes, and both are asymptotically flat, the Kerr black hole is a good option for the method development. The Kerr black hole is a spinning one. We perform this analysis on the Kerr spacetime and we obtain promising results using the covariant phase space analysis. Although we have forced ourselves to use the Bondi fall-off conditions, we find the gauge degrees of freedom that could be g…
The coupling between scalar and vector fields has a long and interesting history. Axions are one key possibility to solve the strong CP problem and axion-like particles could be one solution to the dark matter puzzle. Given the nature of the coupling, and the universality of free fall, nontrivial important effects are expected in regions where gravity is strong. Here, we show that i. A background EM field induces an axionic instability in flat space, for large enough electric fields. Conversely, a homogeneous harmonic axion field induces an instability in the Maxwell sector. When carried over …
The last years have brought upon us a golden age of observational gravitational physics. The several observations by the LIGO/Virgo/KAGRA collaboration about gravitational waves and by the EHT collaboration about the shadow and lensing of light around the supermassive black hole in the centre of M87 will point the scientific community in the correct direction to find an answer to the Kerr hypothesis. In order to follow that direction, the systematic construction and analysis of the physical properties of solutions within General Relativity with additional fields or within modified theories of …
We present a spinning hairy black hole in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. The black hole is characterized by having a single horizon which encloses a curvature singularity and the scalar field is regular everywhere. The mass and angular momentum are shown to be finite. The presence of a scalar field with a slower fall-off at infinity leads an anti-de Sitter asymptotic behavior which differs from the one found by Brown and Henneaux, but has the same symmetry group as in pure gravity. A scalar soliton, which is a finite mass regula…
We have implemented a parallel multigrid solver, to solve the initial data problem for 3+1 General Relativity. This involves solution of elliptic equations derived from the Hamiltonian and the momentum constraints. We use the conformal transverse-traceless method of York and collaborators which consists of a conformal decomposition with a scalar $ϕ$ that adjusts the metric, and a vector potential $w^i$ that adjusts the longitudinal components of the extrinsic curvature. The constraint equations are then solved for these quantities $ϕ$, $w^i$ such that the complete solution fully satisfies the …
The geometry of black hole spacetimes can be probed with exquisite precision in the gravitational-wave window, and possibly also in the optical regime. We study the accretion of bright spots -- objects which emit strongly in the optical or in gravitational waves -- by non-spinning black holes. The emission as the object falls down the hole is dominated by photons or gravitons orbiting the light ring, causing the total luminosity to decrease exponentially as ${\cal L}_o\sim e^{-t/(3\sqrt{3}\,M)}$. Late-time radiation is blueshifted, due to its having been emitted during the infall, trapped at t…
We investigate the spacetime of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as $ g_{μν}=ω^2\tilde g_{μν}$, with $ω$ a dilaton field which contains all the scale dependences. The "unphysical" metric $\tilde g_{μν}$ is related to the $(2+1)$-dimensional Kerr spacetime. The equation for the angular momentum $J$ decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind…
We investigate the development of the magnetic Rayleigh-Taylor instability at the inner edge of an astrophysical disk around a spinning central black hole. We solve the equations of general relativity that govern small amplitude oscillations of a discontinuous interface in a Keplerian disk threaded by an ordered magnetic field, and we derive a stability criterion that depends on the central black hole spin and the accumulated magnetic field. We also compare our results with the results of GR MHD simulations of black hole accretion flows that reach a magnetically arrested state (MAD). We found …
The spin angular momentum $S$ of an isolated Kerr black hole is bounded by the surface area $A$ of its apparent horizon: $8πS \le A$, with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses $M$ and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to $S/M^2 = 0.994$. We measure the area and (using approximate Killing vectors) the spin on the …
Black hole X-ray binaries (BHXRBs) display a wide range of variability phenomena, from long duration spectral state changes to short-term broadband variability and quasi-periodic oscillations (QPOs). A particularly puzzling aspect is the production of QPOs, which -- if properly understood -- could be used as a powerful diagnostic tool of black hole accretion and evolution. In this work we analyse a high resolution three-dimensional general relativistic magnetohydrodynamic simulation of a geometrically thin accretion disk which is tilted by $65^{\circ}$ with respect to the black hole spin axis.…
