General relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source described by the Kerr gravitational field. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The generalized Jacobi equation for the free motion of a test particle is worked out within the Fermi coordinate system established along the world line of a fiducial observer at rest on the symmetry axis of the exterior Kerr background. The nature of the solutions of these equations are investigated in connection with the phenomena associated with astrophysical jets.
Tidal forces are an important feature of General Relativity, which are related to the curvature tensor. We analyze the tidal tensor in Kerr spacetime, with emphasis on the case along the symmetry axis of the Kerr black hole, noting that tidal forces may vanish at a certain point, unlike in the Schwarzschild spacetime, using Boyer-Lindquist coordinates. We study in detail the effects of vanishing tidal forces in a body constituted of dust infalling along the symmetry axis. We find the geodesic deviation equations and solve them, numerically and analytically, for motion along the symmetry axis o…
We generalize to the Kerr spacetime existing self-force results on tidal invariants for particles moving along circular orbits around a Schwarzschild black hole. We obtain linear-in-mass-ratio corrections to the quadratic and cubic electric-type invariants and the quadratic magnetic-type invariant in series of the rotation parameter up to the fourth order. We then construct the eigenvalues of both electric and magnetic tidal tensors and analytically compute them through high post-Newtonian orders.
In this paper, we show the additive separation of the Hamilton-Jacobi equation, present the 4-velocity of the test particles, and attempt to find the equatorial circular photon orbit (ECPO) in the Kerr-Sen-Taub-NUT (KSTN) solution of the low energy limit of heterotic string theory. In the process of trying to find the ECPO, we instead encounter a ring singularity that could be outside the horizon of the KSTN black hole.
We study tidal effects on self-gravitating Newtonian stars rotating around a Kerr black hole in stable circular orbits away from the equatorial plane. Such cases are exemplified by a non-vanishing Carter's constant. Here, we calculate the tidal disruption limit (Roche limit) of the star numerically, in Fermi normal coordinates. The Roche limit is found to depend strongly on the choice of the orbit, and differs significantly from the equatorial plane result as one approaches nearly polar orbits. As expected, this difference is large when the star is close to the black hole (near to the innermos…
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 consider light propagation in a non-magnetized pressureless plasma around a Kerr black hole. We find the necessary and sufficient condition the plasma electron density has to satisfy to guarantee that the Hamilton-Jacobi equation for the light rays is separable, i.e., that a generalized Carter constant exists. For all cases where this condition is satisfied we determine the photon region, i.e., the region in the spacetime where spherical light rays exist. A spherical light ray is a light ray that stays on a sphere $r = \mathrm{constant}$ (in Boyer-Lindquist coordinates). Based on these resu…
Relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source and their solutions are studied. The existence of certain relativistic critical tidal currents are thereby elucidated. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The general tidal equations for the free motion of test particles are worked out with respect to the Kerr background. The analytic solutions of these equations are investigated and the e…
In this paper, we investigate the deflection of a charged particle moving in the equatorial plane of Kerr-Newman spacetime, focusing on weak field limit. To this end, we use the Jacobi geometry, which can be described in three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and $(n+1)$-dimensional stationtary spacetime picture. Based on Randers data and Gauss-Bonnet theorem, we utilize osculating Riemannian manifold method and the generalized Jacobi metric method to study the deflection angle, respectively. In the $(n+1)$-dimensional spacetime picture, the motion o…
An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the world line of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction. For example, one can determine the tidal potential in the neighborhood of the body by constructing a body-fixed frame, which requires Fermi-type coordinates attached to the body itself, the latter being in turn related to the spacetime metric and curvature along the consi…
Within the framework of general relativity, we investigate the tidal acceleration of astrophysical jets relative to the central collapsed configuration ("Kerr source"). We neglect electromagnetic forces throughout. The rest frame of the Kerr source is locally defined via the set of hypothetical static observers in the spacetime exterior to the source. Relative to such a fiducial observer fixed on the rotation axis of the Kerr source, jet particles are tidally accelerated to almost the speed of light if their outflow speed is above a certain threshold, given roughly by one half of the Newtonian…
In this paper the problem of gravitational deflection of relativistic charged massive particles in slowly rotating Kerr-Newman black holes is considered. Toward this purpose we have used two methods: Firstly, we have applied the Gauss-Bonnet theorem (GBT) and the optical geometry to evaluate the deflection angle of charged particles. Secondly, we have presented a detailed analysis of the deflection angle by means of the Hamilton-Jacobi equation recovering the same invariant result for the deflection angle in leading order terms. The crucial point behind the first method is to use the correspon…
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…
In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are re…
We study evolution of the braneworld Kerr--Newman (K-N) naked singularities, namely their mass $M$ , spin $a$, and tidal charge $b$ characterizing the role of the bulk space, due to matter in-falling from Keplerian accretion disk. We construct the evolution in two limiting cases applied to the tidal charge. In the first case we assume $b$ = const during the evolution, in the second one we assume that the dimensionless tidal charge $β\equiv b/M^2$ = const. For positive values of the tidal charge the evolution is equivalent to the case of the standard K-N naked singularity under accretion of ele…
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））
We show that the~braneworld rotating Kerr--Newman black hole and naked singularity spacetimes with both positive and negative braneworld tidal charge parameter can be separated into fourteen classes according to properties of circular geodesics governing the~Keplerian accretion. We determine efficiency of the~Keplerian accretion disks for all braneworld Kerr--Newman spacetimes. We demonstrate occurrence of an~infinitely deep gravitational potential in Kerr--Newman naked singularity spacetimes having the~braneworld dimensionless tidal charge $b \in (1/4,1)$ and the~dimensionless spin $a \in (2\…
Astrophysical phenomena involving massive black holes (BHs) in close binaries are expected to leave detectable signatures in the electromagnetic and gravitational-wave spectrum. Such imprints may provide precious information to probe the space-time around rotating BHs and to reveal new insights on the nature of gravity in the strong-field regime. To support this observational window, it is crucial to develop suitable tests to verify the predictions of General Relativity. In this framework, the metric recently proposed by Johannsen and Psaltis parametrizes strong-field deviations from a Kerr sp…
Relativistic Tidal Transitions of Saturated Kerr Boson Clouds
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, CAS（中国科学院新疆天文台射电天文技术国家重点实验室）；College of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Xinjiang Key Laboratory of Radio Astrophysics（新疆射电天体物理重点实验室）
In this paper, we investigate Hawking radiation of massive spin-1 particles from 5-dimensional Kerr-Gödel spacetime. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the relativistic Proca equation, we obtain the quantum tunneling rate of the massive vector particles. Using the obtained tunneling rate, we show how one impeccably computes the Hawking temperature of the 5-dimensional Kerr-Gödel spacetime.
In this paper, an exact solution of Kerr black hole surrounded by a cloud of strings in Rastall gravity is obtained by Newman-Janis algorithm without complexification, and the influence of the string parameter $a_0$ on the black hole thermodynamics is studied. Furthermore, according to this black hole solution, we investigate the effect of a cloud of strings on gravitational deflection of massive particles. For a receiver and a source at infinite distance from the lens object, we use an osculating Riemannian manifold method. While the distance is finite, we apply the generalized Jacobi metric …
We numerically solve Einstein's equations coupled to a scalar field in the interior of Kerr black holes. We find shock waves form near the inner horizon. The shocks grow exponentially in amplitude and need not be axisymmetric. Observers who pass through the shocks experience exponentially large tidal forces and are accelerated exponentially close to the speed of light.
We analyze the stability of circular geodesics for timelike as well as null geodesics of the Kerr BH spacetime with rotation parameter on the equatorial plane by Lyapunov stability analysis. Also, we verify the results of stability by presenting the phase portrait for both timelike and null geodesics. Further, by reviewing the Kosambi-Cartan-Chern (KCC) theory, we analyze the Jacobi stability for Kerr spacetime and present a comparative study of the methods used for stability analysis of geodesics.
We analyse a rotating regular black hole with asymptotically Minkowski core. This Kerr-like geometry possesses the full "Killing tower" of nontrivial Killing tensor, Killing-Yano tensor, and principal tensor. The Hamilton-Jacobi equation, the Klein-Gordon equation, and Maxwell's equations are separable. Energy-condition-violating physics is pushed into an arbitrarily small region in the deep core. The geometry has a very high level of mathematical tractability; extraction of astrophysical observables falsifiable/verifiable by the observational community is straightforward.
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…
The changes a (negative) tidal charge causes at the phenomenon of superradiance which occurs around rotating black holes are investigated. This is made by computing the amplification factors of massless scalar waves being scattered by the black hole. It is shown that the increase of the tidal charge intensity leads to a considerable enhancement of energy extraction from near-extreme black holes. Such improvement results from the fact that extreme black holes with more negative tidal charges spin faster. Maximum amplification decreases with the increase of the tidal charge intensity if the angu…
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）
In this paper, we study the weak gravitational deflection of relativistic massive particles for a receiver and source at finite distance from the lens in stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we extend the generalized optical metric method to the generalized Jacobi metric method by using the Jacobi-Maupertuis Randers-Finsler metric. More specifically,we apply the Gauss-Bonnet theorem to the generalized Jacobi metric space and then obtain an expression for calculating the deflection angle, which is related to Gaussian curvature of generalized optical met…
The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized stationary and axisymmetric object in four dimensions from the Kaluza-Klein viewpoint. That is, it harbors companion electromagnetic and dilaton fields, thereby showing up the signature of the extra fifth dimension. We explore the separability structure of this spacetime and show that the Hamilton-Jacobi equation for geodesics admits the complete separation of variables only for massless geodesics. This implies the existence of the hidden symmetries in the spacetime, which are generated by the conformal Killing tenso…
