The characteristic difference between a black hole and other exotic compact objects (ECOs) is the presence of the horizon. The horizon of a classical black hole acts as a one-way membrane. Due to this nature, any perturbation on the black hole must satisfy ingoing boundary conditions at the horizon. For an ECO either the horizon is replaced or modified with a surface with non zero reflectivity. This results in a modification of the boundary condition of the perturbation around such systems. In this work, we study how tidal heating of an ECO gets modified due to the presence of a reflective surface and what implication it brings for the gravitational wave observations. We also argue that the position of the reflective surface, $\varepsilon$ $\gtrsim \mathcal{O}(10^{-5})$, can have an observational impact in extreme mass ratio inspirals.
We study the potential of gravitational wave astronomy to observe the quantum aspects of black holes. According to Bekenstein's quantization, we find that black hole area discretization can have observable imprints on the gravitational wave signal from an inspiraling binary black hole. We study the impact of quantization on tidal heating. We model the absorption lines and compute gravitational wave flux due to tidal heating in such a case. By including the quantization we find the dephasing of the gravitational wave, to our knowledge it has never been done before. We discuss the observability …
In this note, using the quasilocal formalism of Brown and York, the flow of energy through a closed surface containing a gravitating physical system is calculated in a way that augments earlier results on the subject by Booth and Creighton. To this end, by performing a variation of the total gravitational Hamiltonian (bulk plus boundary part), it is shown that associated tidal heating and deformation effects generally are larger than expected. This is because this variation leads to previously unrecognized correction terms, including a bulk-to-boundary inflow term that does not appear in the o…
During the early phase of in-spiral of a binary system, the tidal heating of a compact object due to its companion plays a significant role in the determination of the orbital evolution of the binary. The phenomenon depends crucially on the `hairs', as well as on the nature of the compact object. It turns out that the presence of extra dimension affects both these properties, by incorporating an extra tidal charge for braneworld black holes and also by introducing quantum effects, leading to possible existence of exotic compact objects. It turns out that the phasing information from tidal heat…
Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain formula. Purdue and Favata calculated the tidal heating for different classical pseudotensors including Moller and obtained the results all matched with the Newtonian perspective. After re-examined this Moller pseudotensor, we find that there does not exist any tidal heating value. Thus we claim that the relativistic tidal heating is pseudotensor independen…
The increase in the sensitivity of gravitational wave interferometers will bring additional detections of binary black hole and double neutron star mergers. It will also very likely add many merger events of black hole - neutron star binaries. Distinguishing mixed binaries from binary black holes mergers for high mass ratios could be challenging because in this situation the neutron star coalesces with the black hole without experiencing significant disruption. To investigate the transition of mixed binary mergers into those behaving more like binary black hole coalescences, we present results…
In his study of tidal stabilization of fully relativistic neutron stars Thorne showed that the fully relativistic expression for tidal heating is the same as in non-relativistic Newtonian theory. Furthermore, Thorne also noted that the tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Purdue and Favata calculated the tidal heating for a number of classical gravitational pseudotensors including that of Moller, and obtained the result that all of them produced the same (Newtonian) value. However, in a re-examination of the …
Bayesian inference for tidal heating with extreme mass ratio inspirals
Hunan Normal University（湖南师范大学）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；Yangzhou University（扬州大学）；Universidade de São Paulo（圣保罗大学）；Universidade Estadual Paulista（圣保罗州立大学）
Purdue and Favata calculate the tidal heating used certain classical pseudotensors. Booth and Creighton employed the quasi-local mass formalism of Brown and York to demonstrate the same subject. All of them give the result matched with the Newtonian theory. Here we present another Hamiltonian quasi-local boundary expressions and all give the same desired value. This indicates that the tidal heating is unique as Thorne predicted. Moreover, we discovered that the pseudo-tensor method and quasi-local method are fundamentally different.
Imprints of gravitational-wave polarizations on projected tidal tensor in three dimensions
Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo（东京大学宇宙射线研究所卡弗里宇宙物理学与数学研究所）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）；Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理中心）；Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（台湾大学梁林杰宇宙论与粒子天体物理中心）
We study the tidal disruption of neutron stars in black hole-neutron star coalescing binaries. We calculate the critical orbital separation at which the star is disrupted by the black hole tidal field for several equations of state describing the matter inside the neutron star, and for a large set of the binary parameters. When the disruption occurs before the star reaches the innermost stable circular orbit, the gravitational wave (GW) signal emitted by the system is expected to exhibit a cutoff frequency nu_GWtide, which is a distinctive feature of the waveform. We evaluate nu_GWtide and sho…
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 consider possible perturbations of the black hole event horizon induced by matter with spin, extending the derivation of the Hawking-Hartle formula (tidal heating) in the presence of torsion. When specialised to theories with a non-vanishing (pseudo-)traceless component of the (con)torsion tensor, we remarkably find that the tidal heating phenomenon gets modified by additional torsion-dependent terms, in agreement with previous investigations based on Jacobson's spacetime thermodynamics approach. These results lead to relevant phenomenological and theoretical consequences: modifications in …
The combined observation of gravitational and electromagnetic waves from the coalescence of two neutron stars marks the beginning of multi-messenger astronomy with gravitational waves (GWs). The development of accurate gravitational waveform models is a crucial prerequisite to extract information about the properties of the binary system that generated a detected GW signal. In binary neutron star systems (BNS), tidal effects also need to be incorporated in the modeling for an accurate waveform representation. Building on previous work [Phys.Rev.D96 121501], we explore the performance of inspir…
In his study of tidal stabilization of fully relativistic neutron stars Thorne showed that the fully relativistic expression for tidal heating is the same as in non-relativistic Newtonian theory. Furthermore, Thorne also noted that this tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Favata calculated the tidal heating for a number of classical gravitational pseudotensors including that of M$ø$ller, and obtained the result that all of them produced the same (Newtonian) value. After a re-examination of the calculation us…
In 1985 Thorne and Hartle used the Landau-Lifshitz pseudotensor to demonstrate the tidal heating and angular momentum flux for a black hole. Later in 2004, Poisson used the gravitational perturbation method to study a black hole and obtained the same result. Poisson proposed a new idea, that the mass quardupole moment and current quadrupole moment can be written as the rate of change of the tidal gravitational field. Inspired by these two papers, we use the method of Thorne and Hartle to study other classical pseudotensors: Einstein, Bergmann-Thomson, Papapetrou and Weinberg. Moreover, we also…
We present a method for computing the flux of energy through a closed surface containing a gravitating system. This method, which is based on the quasilocal formalism of Brown and York, is illustrated by two applications: a calculation of (i) the energy flux, via gravitational waves, through a surface near infinity and (ii) the tidal heating in the local asymptotic frame of a body interacting with an external tidal field. The second application represents the first use of the quasilocal formalism to study a non-stationary spacetime and shows how such methods can be used to study tidal effects …
When a self-gravitating body (e.g., a neutron star or black hole) interacts with an external tidal field (e.g., that of a binary companion), the interaction can do work on the body, changing its mass-energy. The details of this "tidal heating" are analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge-invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is…
The excitation of $f$-mode in a neutron star member of coalescing binaries accelerates the merger course, and thereby introduces a phase shift in the gravitational waveform. Emphasising on the tidal phase shift by aligned, rotating stars, we provide an accurate, yet economical, method to generate $f$-mode-involved, pre-merger waveforms using realistic spin-modulated $f$-mode frequencies for some viable equations of state. We find for slow-rotating stars that the dephasing effects of the dynamical tides can be uniquely, EOS-independently determined by the direct observables (chirp mass ${\cal M…
The defining feature of a classical black hole is being a perfect absorber. Any evidence showing otherwise would indicate a departure from the standard black-hole picture. Energy and angular momentum absorption by the horizon of a black hole is responsible for tidal heating in a binary. This effect is particularly important in the latest stages of an extreme mass ratio inspiral around a spinning supermassive object, one of the main targets of the future LISA mission. We study how this effect can be used to probe the nature of supermassive objects in a model independent way. We compute the orbi…
We calculate the linear vacuum perturbations of a Kerr black hole surrounded by a slowly-varying external spacetime to third order in the ratio of the black-hole mass to the radius of curvature of the external spacetime. This expansion applies to two relevant physical scenarios: (i) a small Kerr black hole immersed in the gravitational field of a much larger external black hole, and (ii) a Kerr black hole moving slowly around another external black hole of comparable mass. This small-hole/slow-motion approximation allows us to parametrize the perturbation through slowly-varying, time-dependent…
We calculate the energy and angular momentum fluxes across the event horizon of a tidally deformed, rapidly rotating black hole to next-to-leading order in the curvature of the external spacetime. These are expressed in terms of tidal quadrupole moments and their time derivatives, which provide a characterization of a generic tidal environment. As an application of our results, we provide an expression for the energy and angular-momentum fluxes across the horizon when the black hole is a member of a binary system on a slowly-moving, quasi-circular orbit. Our expressions are accurate to 1.5 pos…
The tidal deformability of compact objects by a companion has a detectable imprint in the gravitational waves emitted by a binary system. This effect is governed by the so-called tidal Love numbers. For a particular theory of gravity, these depend solely on the object internal structure and they vanish for black holes in general relativity. A measurement compatible with nonzero tidal Love numbers could thus provide evidence of new physics in the strong-field regime. However, in realistic astrophysical scenarios, compact objects are surrounded by a nonvacuum environment. In this work, we study …
Tidal effects have long ago locked the Moon in synchronous rotation with the Earth and progressively increase the Earth-Moon distance. This "tidal acceleration" hinges on dissipation. Binaries containing black holes may also be tidally accelerated, dissipation being caused by the event horizon - a flexible, viscous one-way membrane. In fact, this process is known for many years under a different guise: superradiance. In General Relativity, tidal acceleration is obscured by gravitational-wave emission. However, when coupling to light scalar degrees of freedom is allowed, an induced dipole momen…
Several quantum-gravity models of compact objects predict microscopic or even Planckian corrections at the horizon scale. We explore the possibility of measuring two model-independent, smoking-gun effects of these corrections in the gravitational waveform of a compact binary, namely the absence of tidal heating and the presence of tidal deformability. For events detectable by the future space-based interferometer LISA, we show that the effect of tidal heating dominates and allows one to constrain putative corrections down to the Planck scale. The measurement of the tidal Love numbers with LISA…
The gravitational wave signal from a binary neutron star merger carries the imprint of the deformability properties of the coalescing bodies, and then of the equation of state of neutron stars. In current models of the waveforms emitted in these events, the contribution of tidal deformation is encoded in a set of parameters, the tidal Love numbers. More refined models include tidal-rotation couplings, described by an additional set of parameters, the rotational tidal Love numbers, which appear in the waveform at $6.5$ post-Newtonian order. For neutron stars with spins as large as $\sim0.1$, we…
The first detection of gravitational waves (GWs) from the binary neutron star (NS) inspiral GW170817 has opened a unique channel for probing the fundamental properties of matter at supra-nuclear densities inaccessible elsewhere in the Universe. This observation yielded the first constraints on the equation of state (EoS) of NS matter from the GW imprint of tidal interactions. Tidal signatures in the GW arise from the response of a matter object to the spacetime curvature sourced by its binary companion. They crucially depend on the EoS and are predominantly characterised by the tidal deformabi…
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 consider tidal encounters between a white dwarf and an intermediate mass black hole. Both weak encounters and those at the threshold of disruption are modeled. The numerical code combines mesh-based hydrodynamics, a spectral method solution of the self-gravity, and a general relativistic Fermi normal coordinate system that follows the star and debris. Fermi normal coordinates provide an expansion of the black hole tidal field that includes quadrupole and higher multipole moments and relativistic corrections. We compute the mass loss from the white dwarf that occurs in weak tidal encounters.…
Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理中心）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN, Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所格兰萨索国家实验室）；Department of Physics and Astronomy, Washington State University（华盛顿州立大学物理与天文系）；School of Physics and Astronomy and Institute for Gravitational Wave Astronomy, University of Birmingham（伯明翰大学物理与天文学院及引力波天文研究所）
Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the 5-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner-Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner-Nordström black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless bot…
The recently discovered system J0651 is the tightest known detached white dwarf (WD) binary. Since it has not yet initiated Roche-lobe overflow, it provides a relatively clean environment for testing our understanding of tidal interactions. I investigate the tidal heating of each WD, parameterized in terms of its tidal Q parameter. Assuming that the heating can be radiated efficiently, the current luminosities are consistent with Q_1=7*10^{10} and Q_2=2*10^7, for the He and C/O WDs, respectively. Conversely, if the observed luminosities are merely from the cooling of the WDs, these estimated v…
The development of a new generation of theoretical models for tidal disruptions is timely, as increasingly diverse events are being captured in surveys of the transient sky. Recently, Gezari et al. reported a discovery of a new class of tidal disruption events: the disruption of a helium-rich stellar core, thought to be a remnant of a red giant (RG) star. Motivated by this discovery and in anticipation of others, we consider tidal interaction of an RG star with a supermassive black hole (SMBH) which leads to the stripping of the stellar envelope and subsequent inspiral of the compact core towa…
With the first detections of binary neutron star mergers by gravitational-wave detectors, it proves timely to consider how the internal structure of neutron stars affects the way in which they can be asymmetrically deformed. Such deformations may leave measurable imprints on gravitational-wave signals and can be sourced through tidal interactions or the formation of mountains. We detail the formalism that describes fully-relativistic neutron star models with elastic crusts undergoing static perturbations. This formalism primes the problem for studies into a variety of mechanisms that can defor…
Tidal forces cause inspiralling binary neutron stars to deform, leaving a measurable imprint on the gravitational waves they emit. The induced stellar multipoles are an added source of gravitational radiation and modify the orbital dynamics, producing a slight acceleration of the coalescence which manifests as a phase shift in the waveform relative to point-particles. The dominant piece of this tidal phase comes from the mass quadrupoles, which contribute at fifth post-Newtonian order (5PN). Current quadrupoles and mass octupoles contribute at higher orders. For spinning neutron stars, additio…
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 tidal deformations of neutron stars within an inspiraling compact binary alter the orbital dynamics, imprinting a signature on the gravitational wave signal. Modeling this signal could be done with numerical-relativity simulations, but these are too computationally expensive for many applications. Analytic post-Newtonian treatments are limited by unknown higher-order nontidal terms. This paper further builds upon the "tidal splicing" model in which post-Newtonian tidal terms are "spliced" onto numerical relativity simulations of black-hole binaries. We improve on previous treatments of tid…
Black holes can be inserted in very rich astrophysical environments, such as accretion disks. Although isolated black holes are simple objects in general relativity, their accretion disks may significantly enrich the field configurations of their surroundings. Alternative theories of gravity can lead to novel black hole solutions, which can be represented by small deviations in the metric due to an effective stress-energy tensor. Among the key aspects of the interaction of black holes with their surroundings, stand tidal forces phenomena. We study the tidal forces of spherically symmetric blac…
The Laser Interferometer Space Antenna (LISA) will open the low-frequency (0.1-100 mHz) part of the gravitational wave spectrum to direct observation. Of order 3600 galactic close binary white dwarfs will be individually resolvable in its all-sky spectrum, of which a dozen systems are expected to be on the verge of merger, showing the effects of strong tidal heating and/or early onset of tidal mass transfer. Optical study of these systems would provide important insights into tidal dissipation mechanisms, and internal heating in merging white dwarfs that sets ignition conditions for potential …
