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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.
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.
Physics Letters B, 2013
The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a limitation of the classical theory. While we do not yet have any solid theory of quantum gravity, toy models of black hole solutions without singularities have been proposed. So far, there are only non-rotating regular black holes in the literature. These metrics can be hardly tested by astrophysical observations, as the black hole spin plays a fundamental role in any astrophysical process. In this letter, we apply the Newman-Janis algorithm to the Hayward and to the Bardeen black hole metrics. In both cases, we obtain a family of rotating solutions. Every solution corresponds to a different matter configuration. Each family has one solution with special properties, which can be written in Kerr-like form in Boyer-Lindquist coordinates. These special solutions are of Petrov type D, they are singularity free, but they violate the weak energy condition for a non-vanishing spin and their curvature invariants have different values at r = 0 depending on the way one approaches the origin. We propose a natural prescription to have rotating solutions with a minimal violation of the weak energy condition and without the questionable property of the curvature invariants at the origin.
The Cauchy horizon singularity inside Kerr black holes
Bulletin of the American Physical Society, 2016
Submitted for the APR16 Meeting of The American Physical Society The Cauchy horizon singularity inside Kerr black holes LIOR M. BURKO, Georgia Gwinnett College, GAURAV KHANNA, University of Massachusetts Dartmouth-The numerical technology that allows for the careful evolution of linearized fields inside Kerr black holes and the study of their behavior approaching the Cauchy horizon singularity includes a number of interesting aspects. The latter include compactified hyperboloidal coordinates and foliation, mixed type hyperbolic-elliptic PDE, and initial data evolution where all equal-coordinate hypersurfaces are spacelike. We review the need for the numerical technology that allows for the solution of the spin-2 Teukolsky equation inside Kerr black holes, and discuss the main features thereof. We present new results about the numerical properties of the Cauchy horizon singularity and their correspondence with the predictions of perturbative analysis. We then discuss present directions of study, which include the subdominant azimuthal modes, approaching the Cauchy horizon singularity along timelike directions, approaching the Marolf-Ori ("outflying") singularity and the studying the fields along the Cauchy horizon.
The eye of the storm: a regular Kerr black hole
Journal of Cosmology and Astroparticle Physics, 2022
We analyse in some detail a highly tractable non-singular modification of the Kerr geometry, dubbed the “eye of the storm” — a rotating regular black hole with an asymptotically Minkowski core. This is achieved by “exponentially suppressing” the mass parameter in the Kerr spacetime: m → m e-ℓ/r . The single suppression parameter ℓ quantifies the deviation from the usual Kerr spacetime. Some of the classical energy conditions are globally satisfied, whilst certain choices for ℓ force any energy-condition-violating physics into the deep core. The geometry possesses the full “Killing tower” of principal tensor, Killing-Yano tensor, and nontrivial Killing tensor, with associated Carter constant; hence the Hamilton-Jacobi equations are separable, and the geodesics integrable. Both the Klein-Gordon equation and Maxwell's equations are also separable on this candidate spacetime. The tightly controlled deviation from Kerr renders the physics extraordinarily tractable when compared with ...
On the possible spacetime structures of rotating loop quantum black holes
International Journal of Geometric Methods in Modern Physics
To date, a mathematically consistent construction of effective rotating black hole models in the context of Loop Quantum Gravity (LQG) is still lacking. In this work, we start with the assumption that rotating LQG black hole metrics can be effectively obtained using Newman–Janis Algorithm. Then, based on a few extra fair assumptions on the seed metric functions, we make a conjecture on what a rotating LQG black hole would generically look like. Our general arguments and conclusions can be supported by some known specific examples in the literature.
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.
Spinning higher dimensional Einstein–Yang–Mills black holes
The European Physical Journal C, 2014
We construct a Kerr-Newman-like spacetimes starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis. The new metrics are HD generalization of Kerr-Newman spacetimes which has a geometry precisely that of Kerr-Newman in 4D corresponding to Yang-Mills (YM) gauge charge, but the sign of charge term gets flipped in the HD spacetimes. It is interesting to note that gravitational contribution of YM gauge charge, in HD, is indeed opposite (attractive rather than repulsive) that of Maxwell charge. The effect of YM gauge charge on the structure and location of static limit surface and apparent horizon is discussed. We find that static limit surfaces become less prolate with increase in dimensions and are also sensitive to YM gauge charge thereby affecting the shape of ergosphere. We also analyze some thermodynamical properties of these BHs.