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The Kerr/CFT correspondence

Monica Guica, Thomas Hartman, Wei Song, and Andrew Strominger
Phys. Rev. D 80, 124008 – Published 7 December 2009
Physics logo See Viewpoint: Are black holes really two dimensional?

Abstract

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge cL=12J. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature TL=12π and conjugate energy given by the zero mode generator, L0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy Smicro=2πJ for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy Smacro=Area4G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge cL=12J, and, in particular, that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with cL2×1079.

  • Received 4 September 2009

DOI:https://doi.org/10.1103/PhysRevD.80.124008

©2009 American Physical Society

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Are black holes really two dimensional?

Published 7 December 2009

The insights of a provocative connection between general relativity and quantum field theory, called the AdS/CFT correspondence, have been extended to rotating black holes that can occur astrophysically.

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Authors & Affiliations

Monica Guica1, Thomas Hartman2, Wei Song2,*, and Andrew Strominger2

  • 1Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie-Paris 6; CNRS Boîte 126, 4 Pl. Jussieu, 75252 Paris Cedex 05, France
  • 2Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA

  • *On leave from the Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China.

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Issue

Vol. 80, Iss. 12 — 15 December 2009

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