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 heating in the gravitational wave waveform can constrain the tidal charge inherited from extra dimension to a value $\sim 10^{-6}$, the most stringent constraint, to date. Moreover, second order effects in tidal heating for exotic compact objects, also reveals an oscillatory behaviour with respect to spin, which has unique signatures.
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…
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 …
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.
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 …
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…
There is a growing interest in investigating modified theories of gravity, primarily, with the aim of explaining the universe's accelerated expansion, which has been confirmed by several independent observations. Compact objects, like neutron stars, exhibit strong gravity effects and therefore are used to study modified gravity theories. We use the $f(R)=R+aR^2$ model, where R is the Ricci scalar and $a$ is a free parameter. This model has been studied both perturbatively and non-perturbatively. However, it was found that perturbative methods results in nonphysical solutions for the neutron st…
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…
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…
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 sur…
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…
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）
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…
This paper investigates the various spherically symmetric wormhole solutions in the presence of tidal forces and applies numerous methods, such as test particle orbital dynamics, ray-tracing and microlensing. We make the theoretical predictions on the test particle orbital motion around the tidal wormholes with the use of normalized by $\mathcal{L}^2$ effective potential. In order to obtain the ray-tracing images (of both geometrically thin and thick accretion disks, relativistic jets), we properly modify the open source $\texttt{GYOTO}$ code with python interface. We applied this techniques t…
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 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…
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 …
Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizo…
The moment of inertia, the spin-induced quadrupole moment, and the tidal Love number of neutron-star and quark-star models are related through some relations which depend only mildly on the stellar equation of state. These "I-Love-Q" relations have important implications for astrophysics and gravitational-wave astronomy. An interesting problem is whether similar relations hold for other compact objects and how they approach the black-hole limit. To answer these questions, here we investigate the deformation properties of a large class of thin-shell gravastars, which are exotic compact objects …
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）
In the context of higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, are more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, inherited from the projection of the higher dimensional Weyl tensor onto the four dimensional spacetime we live in. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact object…
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…
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…
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…
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 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 …
