Exact solutions for a system of two counter-rotating black holes (original) (raw)
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On the interaction between two Kerr black holes
Journal of High Energy Physics, 2008
The double-Kerr solution is generated using both a Bäcklund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z φ 2 invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J| = cM 2 , where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.
The symmetries of Kerr black holes
Communications in Mathematical Physics, 1973
The Kerr solution describes, in Einstein's theory, the gravitational field of a rotating black hole. The axial symmetry and stationarity of the solution are shown here to arise in a simple way from properties of the curvature tensor.
The general vacuum solution and the new hairs to the Kerr black hole
2001
We have obtained the most general solution of the Einstein vacuum equation for the axially symmetric stationary metric in which the Klein - Gordon equation is separable. It has four parameters of which the two are familiar mass and rotation (or NUT-like parameter) while the other two are new and dimensionless, and can survive only when the rotation parameter is non-zero. The general solution includes the Kerr black hole which would now have two new hairs arising at the cost of asymptotic flatness
Annals of Physics, 2020
The Newman-Janis (NJ) method is a prescription to derive the Kerr space-time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers-Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional (d > 6) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the fivedimensional MP metric with two arbitrary angular momenta by using the Kerr-Schild form of the metric and quaternions. Then, we present another new twostep version of the NJ approach without using quaternions that generate the five-dimensional MP metric with equal angular momenta. Finally, the extension of the later procedure is explained for the higher odd-dimensional rotating black holes (d > 5) with equal angular momenta.
The Kerr–Newman–Gödel black hole
Classical and Quantum Gravity, 2003
By applying a set of Hassan-Sen transformations and string dualities to the Kerr-Gödel solution of minimal D = 5 supergravity we derive a four parameter family of five dimensional solutions in type II string theory. They describe rotating, charged black holes in a rotating background. For zero background rotation, the solution is D = 5 Kerr-Newman; for zero charge it is Kerr-Gödel. In a particular extremal limit the solution describes an asymptotically Gödel BMPV black hole. * by the quantum states . The BMPV spacetime can only be interpreted as a black hole for sufficiently small values of angular momentum; otherwise there is no horizon and the spacetime becomes a non-singular repulson with Closed Timelike Curves passing through any point. On the string theory side unitarity is violated when this happens .
Metric of two balancing Kerr particles in physical parametrization
Physical Review D, 2015
The present paper aims at elaborating a completely physical representation for the general 4parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black hole-superextreme object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordström configurations.
The Kerr spacetime: rotating black holes in general relativity
2009
Click here if your download doesn"t start automatically The Kerr Spacetime: Rotating Black Holes in General Relativity The Kerr Spacetime: Rotating Black Holes in General Relativity Rotating black holes, as described by the Kerr space-time, are the key to understanding the most violent and energetic phenomena in the Universe, from the core collapse of massive supernova explosions producing powerful bursts of gamma rays, to supermassive black hole engines that power quasars and other active galactic nuclei. This book is a unique, comprehensive overview of the Kerr space-time, with original contributions and historical accounts from researchers who have pioneered the theory and observation of black holes, and Roy Kerr's own description of his 1963 discovery. It covers all aspects of rotating black holes, from mathematical relativity to astrophysical applications and observations, and current theoretical frontiers. This book provides an excellent introduction and survey of the Kerr space-time for researchers and graduate students across the spectrum of observational and theoretical astrophysics, general relativity, and high-energy physics.
Angular Eigenvalues of Higher-Dimensional Kerr(A)dS Black Holes with Two Rotations
2011
In this paper, following the work of Chen, L\"u and Pope, we present the general metric for Kerr-(A)dS black holes with two rotations. The corresponding Klein-Gordon equation is separated explicitly, from which we develop perturbative expansions for the angular eigenvalues in powers of the rotation parameters with Dgeq6D\geq 6Dgeq6.
Extreme Kerr black holes are non-unique
Bulletin of the American Physical Society, 2021
Dartmouth-The uniqueness of classical black holes-the celebrated "no hair theorems"-guarantee that no parameters other than the mass, charge, and spin angular momentum of stationary black holes can me measured. For a family of scalar or gravitational perturbations of an extreme Kerr black hole, whose members vary only in the radial location of the center of the initial packet, we demonstrate a linear relation of a generalized Ori pre-factor-a certain expression obtained from the late-time expansion or the perturbation field at finite distances-and the Aretakis conserved charge. It can be established that there is an Aretakis conserved charge for scalar or gravitational perturbations of extreme Kerr black holes. This conclusion, in addition to the calculation of the Aretakis charge, can be made from measurements at a finite distance: Extreme Kerr black holes have gravitational hair that can be measured at finite distances, and violates the uniqueness theorems. This gravitational hair can in principle be detected by gravitational-wave detectors. We identify the failure of the uniqueness theorems to apply with the time dependence of extreme black holes along their event horizons (Aretakis behavior of certain transverse derivatives), although external perturbations decay.