skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes

Abstract

A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a nonflat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in D-dimensional space-time with D-2 commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.

Authors:
 [1]
  1. Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia, and Novosibirsk University, 630090, Novosibirsk (Russian Federation)
Publication Date:
OSTI Identifier:
20776742
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044004; (c) 2006 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; BLACK HOLES; COSMOLOGY; EINSTEIN FIELD EQUATIONS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; SOLITONS; SPACE-TIME; SYMMETRY; VECTORS

Citation Formats

Pomeransky, A.A.. Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.044004.
Pomeransky, A.A.. Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes. United States. doi:10.1103/PhysRevD.73.044004.
Pomeransky, A.A.. Wed . "Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes". United States. doi:10.1103/PhysRevD.73.044004.
@article{osti_20776742,
title = {Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes},
author = {Pomeransky, A.A.},
abstractNote = {A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a nonflat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in D-dimensional space-time with D-2 commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.},
doi = {10.1103/PhysRevD.73.044004},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • We investigate the stability of higher dimensional rotating black holes against scalar perturbations. In particular, we make a thorough numerical and analytical analysis of six dimensional black holes, not only in the low rotation regime but in the high rotation regime as well. Our results suggest that higher dimensional Kerr black holes are stable against scalar perturbations, even in the ultraspinning regime.
  • We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, a{sub i}=a, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters a{sub i} take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favoredmore » against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single nonzero rotation parameter. The five-dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a nonrotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six-dimensional case is marginal.« less
  • Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case, we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceedsmore » the speed of light from the point of view of the conformal boundary. We suggest that the end point of the instability may be a stationary, nonaxisymmetric black hole.« less
  • In this paper, with an appropriate combination of three Liouville-type dilaton potentials, we obtain the higher dimensional charged slowly rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime. The angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton coupling constant. It is shown that the dilaton field modifies the gyromagnetic ratio of the rotating dilaton black holes.
  • We present numerical evidences for the existence of rotating black holes in d-dimensional Einstein-Maxwell theory with a cosmological constant and for an odd number of dimensions. The metric used possesses (d+1)/2 Killing vectors and the black holes have (d-1)/2 equal angular momenta. The Schwarzschild-like coordinate system used clearly reveals the influence of the electromagnetic field on the vacuum black holes where analytic expressions are available. The domain of existence of the charged rotating black holes is then characterized for both signs of the cosmological constant. The generic solutions are specified by their event horizon and by two additional parameters: themore » magnetic field and the angular velocity at the horizon. The dependence of several physical quantities - surface gravity, mass, angular momentum, etc. - is studied as a function of these parameters; Smarr-like relations are derived.« less