Microscopic entropy of the three-dimensional rotating black hole of Bergshoeff-Hohm-Townsend massive gravity

Gaston Giribet, Julio Oliva, David Tempo, and Ricardo Troncoso
Phys. Rev. D 80, 124046 – Published 30 December 2009

Abstract

Asymptotically anti–de Sitter rotating black holes for the Bergshoeff-Hohm-Townsend massive gravity theory in three dimensions are considered. In the special case when the theory admits a unique maximally symmetric solution, apart from the mass and the angular momentum, the black hole is described by an independent “gravitational hair” parameter, which provides a negative lower bound for the mass. This bound is saturated at the extremal case, and since the temperature and the semiclassical entropy vanish, it is naturally regarded as the ground state. The absence of a global charge associated with the gravitational hair parameter reflects itself through the first law of thermodynamics in the fact that the variation of this parameter can be consistently reabsorbed by a shift of the global charges, giving further support to consider the extremal case as the ground state. The rotating black hole fits within relaxed asymptotic conditions as compared with the ones of Brown and Henneaux, such that they are invariant under the standard asymptotic symmetries spanned by two copies of the Virasoro generators, and the algebra of the conserved charges acquires a central extension. Then it is shown that Strominger’s holographic computation for general relativity can also be extended to the Bergshoeff-Hohm-Townsend theory; i.e., assuming that the quantum theory could be consistently described by a dual conformal field theory at the boundary, the black hole entropy can be microscopically computed from the asymptotic growth of the number of states according to Cardy’s formula, in exact agreement with the semiclassical result.

  • Received 24 September 2009

DOI:https://doi.org/10.1103/PhysRevD.80.124046

©2009 American Physical Society

Authors & Affiliations

Gaston Giribet1, Julio Oliva2,3, David Tempo2,4,5, and Ricardo Troncoso2,6

  • 1Center for Cosmology and Particle Physics, New York University, 4 Washington Place NY10003, New York, USA
  • 2Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia, Chile
  • 3Instituto de Física, Facultad de Ciencias, Universidad Austral de Chile, Casilla 567, Valdivia, Chile
  • 4Departamento de Física, Universidad de Concepción, Casilla, 160-C, Concepción, Chile
  • 5Physique théorique et mathématique, Université Libre de Bruxelles, ULB Campus Plaine CP 231, B-1050 Bruxelles, Belgium
  • 6Centro de Ingeniería de la Innovación del CECS (CIN), Valdivia, Chile

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Issue

Vol. 80, Iss. 12 — 15 December 2009

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