A sum rule for tidal Love number is derived from quantum field theory computations, which relates tidal susceptibility of a spinless body to transition rates of its single graviton emission processes. An analogous sum rule for electromagnetism is given as an example, which is substantiated by comparing to the solved problem of the hydrogen atom. Based on the semiclassical Hawking radiation spectrum, a finite nonvanishing value for quantum corrections to the Love number of Schwarzschild black holes in general relativity is computed using the sum rule, which is known to classically vanish.
In this note, we analyze black holes solutions under R3 corrections, which is the leading correction induced by quantum corrections in four-dimensions. We showed that perturbations around this black hole background will lead to non-zero tidal Love number (TLN). This further accentuates the \unnaturalness" of the vanishing TLN for Schwarzschild black hole under Einstein-Hilbert action.
We calculate the tidal Love numbers of black holes and neutron stars in the presence of higher dimensions. The perturbation equations around an arbitrary static and spherically symmetric metric for the even parity modes are presented in the context of an effective four-dimensional theory on the brane. This subsequently leads to the sought expression for the tidal Love number for black holes in the presence of extra spatial dimensions. Surprisingly, these numbers are non-zero and, more importantly, negative. We extend our method to determine the tidal Love number of neutron stars in a spacetime…
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…
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）
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院理论物理甘肃省重点实验室兰州理论物理中心）
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. Spec…
Proca stars (arXiv:1508.05395) are everywhere regular, asymptotically flat self-gravitating solitons composed of complex, massive vector bosons, forming a macroscopic, star-sized, Bose-Einstein condensate. They have been suggested as a classical, dynamical model of exotic compact objects, black hole mimickers and dark matter candidates. In spherical symmetry, they are qualitatively similar to their scalar cousins, the standard (scalar) boson stars in all respects studied so far. Here we study the tidal deformability and the quadrupolar tidal Love numbers, both electric-type and magnetic-type, …
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）
We study the tidal deformations of various known black hole and wormhole solutions in a simple context of warped compactification -- Randall-Sundrum theory in which the four-dimensional spacetime geometry is that of a brane embedded in five-dimensional Anti-de Sitter spacetime. The linearized gravitational perturbation theory generically reduces to either an inhomogeneous second-order ODE or a homogeneous third-order ODE of which indicial roots associated with an expansion about asymptotic infinity can be related to Tidal Love Numbers. We describe various tidal-deformed metrics, classify their…
Institut des Hautes Études Scientifiques（高等科学研究所）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（理论科学国际中心，塔塔基础研究所）
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…
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 …
Nonlinear Relativistic Tidal Response of Neutron Stars
Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马大学物理系与INFN罗马第一分部）；Department of Physics, Center for Theoretical Physics, Columbia University（哥伦比亚大学理论物理中心物理系）；Université Paris Cité, CNRS, Astroparticule et Cosmologie（巴黎西岱大学、法国国家科学研究中心粒子物理与宇宙学）；Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique（巴黎萨克雷大学、法国国家科学研究中心、法国原子能和替代能源委员会理论物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Fermionic Love number of Reissner-Nordström black holes
School of Physics and Astronomy, China West Normal University（西华师范大学物理与天文学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；International of Theoretical Physics, Chinese Academy of Science（中国科学院理论物理国际中心）；Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra sh(1) = sl$(2,\mathbb{R}) \ltimes \mathcal{H}$. The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black…
Utah State University（犹他州立大学）；Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学UAM-CSIC理论物理研究所）；Université Paris Cité, CNRS, Astroparticule et Cosmologie（巴黎西岱大学CNRS天体粒子与宇宙学）；University of Virginia（弗吉尼亚大学）
We investigate some properties of n(\ge 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C^2 vacuum solutions are classified into four types: (i) Schwarzs…
Indian Association for the Cultivation of Science（印度科学培养协会）；Sapienza Università di Roma（罗马第一大学）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；University of Chinese Academy of Sciences（中国科学院大学）
Love at the String Scale: Tidal Deformability Across the Black Hole-String Transition
Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究所）；Universitat de Barcelona（巴塞罗那大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
Universidade Federal do ABC（ABC联邦大学）；IFT - UNESP & ICTP - SAIFR（圣保罗州立大学物理研究所与ICTP-SAIFR）；CMCC, Universidade Federal do ABC（ABC联邦大学气候中心）；ITP, TU Wien（维也纳工业大学理论物理研究所）
We show that perturbations of massless fields in the Kerr black hole background enjoy a hidden $SL(2,\mathbb{R})\times {U}(1)$ ("Love") symmetry in the properly defined near zone approximation. Love symmetry mixes IR and UV modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses. Generators of the Love symmetry are globally well defined and have a smooth Schwarzschild limit. Generic regular solutions of the near zone Teukolsky equation form infinite-dimensional $SL(2,\mathbb{R})$ representations. In some special cases ($\hat{\ell}$ parameter is an…
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 …
According to the black hole membrane paradigm, the black hole event horizon behaves like a 2+1 dimensional fluid. The fluid has nonzero momentum density but zero velocity. As a result, it does not respond to tidal forces in the usual way. In this note, we point out that this unusual behavior can be traced back to an emergent, near-horizon Carroll symmetry (the Carroll group is the $c\rightarrow 0$ limit of the Poincaré group). For Schwarzschild black holes in $d=4$ general relativity, we relate the vanishing of the black hole fluid's velocity to vanishing of the black hole's Love numbers. This…
