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Title: Electromagnetic properties of Kerr-anti-de Sitter black holes

Abstract

We examine the electromagnetic properties of Kerr-anti-de Sitter (Kerr-AdS) black holes in four and higher spacetime dimensions. Assuming that the black holes may carry a test electric charge we show that the Killing one-form which represents the difference between the timelike generators in the spacetime and in the reference background can be used as a potential one-form for the associated electromagnetic field. In four dimensions the potential one-form and the Kerr-AdS metric with properly rescaled mass parameter solve the Einstein-Maxwell equations, thereby resulting in the familiar Kerr-Newman-AdS solution. We solve the quartic equation governing the location of the event horizons of the Kerr-Newman-AdS black holes and present closed analytic expressions for the radii of the horizons. We also compute the gyromagnetic ratio for these black holes and show that it corresponds to g=2 just as for ordinary black holes in asymptotically flat spacetime. Next, we compute the gyromagnetic ratio for the Kerr-AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe ismore » rotating at the speed of light, it tends to g=2 irrespective of the spacetime dimension. Finally, we consider the case of a five-dimensional Kerr-AdS black hole with two angular momenta and show that it possesses two distinct gyromagnetic ratios in accordance with its two orthogonal two-planes of rotation. In the special case of two equal angular momenta, the two gyromagnetic ratios merge into one leading to g=4 at the maximum angular velocities of rotation.« less

Authors:
 [1]
  1. Feza Guersey Institute, P. K. 6 Cengelkoey, 34684 Istanbul (Turkey)
Publication Date:
OSTI Identifier:
21020410
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084041; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; ANGULAR VELOCITY; BLACK HOLES; COSMOLOGY; DE SITTER GROUP; EINSTEIN-MAXWELL EQUATIONS; ELECTRIC CHARGES; ELECTROMAGNETIC FIELDS; GYROMAGNETIC RATIO; KERR METRIC; MASS; MATHEMATICAL SOLUTIONS; POTENTIALS; ROTATION; SPACE-TIME; UNIVERSE

Citation Formats

Aliev, Alikram N. Electromagnetic properties of Kerr-anti-de Sitter black holes. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.084041.
Aliev, Alikram N. Electromagnetic properties of Kerr-anti-de Sitter black holes. United States. doi:10.1103/PHYSREVD.75.084041.
Aliev, Alikram N. Sun . "Electromagnetic properties of Kerr-anti-de Sitter black holes". United States. doi:10.1103/PHYSREVD.75.084041.
@article{osti_21020410,
title = {Electromagnetic properties of Kerr-anti-de Sitter black holes},
author = {Aliev, Alikram N.},
abstractNote = {We examine the electromagnetic properties of Kerr-anti-de Sitter (Kerr-AdS) black holes in four and higher spacetime dimensions. Assuming that the black holes may carry a test electric charge we show that the Killing one-form which represents the difference between the timelike generators in the spacetime and in the reference background can be used as a potential one-form for the associated electromagnetic field. In four dimensions the potential one-form and the Kerr-AdS metric with properly rescaled mass parameter solve the Einstein-Maxwell equations, thereby resulting in the familiar Kerr-Newman-AdS solution. We solve the quartic equation governing the location of the event horizons of the Kerr-Newman-AdS black holes and present closed analytic expressions for the radii of the horizons. We also compute the gyromagnetic ratio for these black holes and show that it corresponds to g=2 just as for ordinary black holes in asymptotically flat spacetime. Next, we compute the gyromagnetic ratio for the Kerr-AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe is rotating at the speed of light, it tends to g=2 irrespective of the spacetime dimension. Finally, we consider the case of a five-dimensional Kerr-AdS black hole with two angular momenta and show that it possesses two distinct gyromagnetic ratios in accordance with its two orthogonal two-planes of rotation. In the special case of two equal angular momenta, the two gyromagnetic ratios merge into one leading to g=4 at the maximum angular velocities of rotation.},
doi = {10.1103/PHYSREVD.75.084041},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.
  • A class of exact solutions of the Einstein-Maxwell equations is presented which describes an accelerating and rotating charged black hole in an asymptotically de Sitter or anti-de Sitter universe. The metric is presented in a new and convenient form in which the meaning of the parameters is clearly identified, and from which the physical properties of the solution can readily be interpreted.
  • We calculate the total flux of Hawking radiation from Kerr-(anti)de Sitter black holes by using gravitational anomaly method developed in [S. P. Robinson and F. Wilczek, Phys. Rev. Lett. 95, 011303 (2005)]. We consider the general Kerr-(anti)de Sitter black holes in arbitrary D dimensions with the maximal number [D/2] of independent rotating parameters. We find that the physics near the horizon can be described by an infinite collection of (1+1)-dimensional quantum fields coupled to a set of gauge fields with charges proportional to the azimuthal angular momentums m{sub i}. With the requirement of anomaly cancellation and regularity at the horizon,more » the Hawking radiation is determined.« less
  • We study the thermodynamic stability of the Kerr-anti-de Sitter black hole from the perturbative corrections to the gravitational partition function. The line of critical stability is identified by the appearance of a negative mode of the Euclidean action that renders the partition function ill defined. The eigenvalue problem, consisting of a system of three coupled partial differential equations for the metric perturbations, is solved numerically. The agreement with the standard condition of thermodynamic stability in the grand-canonical ensemble is remarkable. The results illustrate the physical significance of gravitational partition functions for rotating spacetimes beyond the instanton approximation. At a classicalmore » level, the results also imply that the Gregory-Laflamme instability of the Kerr string persists up to extremality, the range of unstable modes increasing with the angular momentum.« less
  • Based on Sen's entropy function formalism, we consider the Bekenstein-Hawking entropy of the extremal Kerr-(anti-)de Sitter black holes in 4-dimensions. Unlike the extremal Kerr black hole case with flat asymptotic geometry, where the Bekenstein-Hawking entropy S is proportional to the angular momentum J, we get a quartic algebraic relation between S and J by using the known solution to the Einstein equation. We recover the same relation in the entropy function formalism. Instead of full geometry, we write down an ansatz for the near horizon geometry only. The exact form of the unknown functions and parameters in the ansatz aremore » obtained by solving the differential equations which extremize the entropy function. The results agree with the nontrivial relation between S and J. We also study the Gauss-Bonnet correction to the entropy exploiting the entropy function formalism. We show that the term, though being topological thus does not affect the solution, contributes a constant addition to the entropy because the term shifts the Hamiltonian by that amount.« less