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 tensor, i.e., observer-dependent super-energy density and super-Poynting vector, are investigated too.
The observer-dependent tidal effects associated with the electric and magnetic parts of the Riemann tensor with respect to an arbitrary family of observers are discussed in a general spacetime in terms of certain "tidal indicators." The features of such indicators are then explored by specializing our considerations to the family of stationary circularly rotating observers in the equatorial plane of the Kerr spacetime. There exist a number of observer families which are special for several reasons and for each of them such indicators are evaluated. The transformation laws of tidal indicators w…
Recent gravitational-wave observations have begun to constrain the internal physics of neutron stars. However, current detection searches for neutron star systems assume that potential neutron stars are low-mass black holes, ignoring any affect on the gravitational-wave signal due to the internal neutron-star physics. We wish to create a template bank of binary neutron star waveforms including the effect of tidal deformability. However, we find that the Fisher matrix, which is commonly used to approximate match calculations when placing template banks, is unsuitable to predict the match betwee…
The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale R^{-1}, where R is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order R^{-2}, and it is carried out through order R^{-4}. The metric is parameterized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor…
Here we consider two phenomena in the vicinity of a black hole deformed by the tidal gravitational force of surrounding matter and by a strong magnetic field: equatorial motion of charged particles and the decay of a test scalar field. We were able to analyze both phenomena with analytical and simple numerical tools, which was unexpected given the low symmetry of the system. We show that both the tidal gravitational force and the magnetic field strongly enhance the release of the binding energy for the matter spiralling into the black hole. In the presence of the magnetic field, the left and r…
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 …
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…
The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes
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）；Niels Bohr Institute（尼尔斯·玻尔研究所）；Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等技术学院）
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…
We investigate tidal effects produced in the spacetime of Schwarzschild black hole in holographic massive gravity, which has two additional mass parameters due to massive gravitons. As a result, we have obtained that massive gravitons affect the angular component of the tidal force, while the radial component has the same form with the one in massless gravity. On the other hand, by solving the geodesic deviation equations, we have found that radial components of two nearby geodesics keep tightening while falling into the black hole and after passing the event horizons get abruptly infinitely s…
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…
Tools from scattering amplitudes and effective field theory have recently been repurposed to derive state-of-the-art results for the black hole binary inspiral in the post-Minkowskian expansion. In the present work we extend this approach to include the tidal effects of mass and current quadrupoles on the conservative dynamics of non-spinning neutron star mergers. We compute the leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles. Our expressio…
We study tidal stripping of fuzzy dark matter (FDM) subhalo cores using simulations of the Schrödinger-Poisson equations and analyze the dynamics of tidal disruption, highlighting the differences with standard cold dark matter. Mass loss outside of the tidal radius forces the core to relax into a less compact configuration, lowering the tidal radius. As the characteristic radius of a solitonic core scales inversely with its mass, tidal stripping results in a runaway effect and rapid tidal disruption of the core once its central density drops below $4.5$ times the average density of the host wi…
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…
Tidal perturbations play an important role in the study of the dynamics in the classical two-body system. Understanding tidal effects in strong-field regions may allow one to use gravitational-wave or electromagnetic observations to locate or constraint the location of possible companions. Here, we investigate how timelike and null geodesics of a Schwarzschild black hole are affected in the presence of a companion. There is a panoply of new effects. In some limiting cases, we find analytical solutions for closed null or timelike geodesics. Our results show that light ring period as measured by…
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））
Tidally-enhanced resonances in extreme-mass-ratio inspirals: A tertiary path to chaos
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等理工学院）；Theoretical Astrophysics, Institute for Astronomy and Astrophysics, University of Tübingen（蒂宾根大学天文与天体物理研究所）；School of Applied Mathematical and Physical Sciences – SEMFE, Physics Department, National Technical University of Athens（雅典国立技术大学应用数理科学与物理学院）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；INFN, Sezione di Roma（意大利国家核物理研究院罗马分部）；Birla Institute of Technology and Science Pilani（比拉理工科学皮拉尼分校）
Deformed Schwarzschild horizons in second-order perturbation theory: mass, geometry, and teleology
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen（格罗宁根大学伯努利数学、计算机科学与人工智能研究所）；School of Mathematical Sciences and STAG Research Centre, University of Southampton（南安普顿大学数学科学学院和STAG研究中心）；Institute for Physics and Astronomy, University of Potsdam（波茨坦大学物理与天文学研究所）
