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The Kerr/CFT Correspondence

By Monica Guica, Thomas Hartman, Wei Song and Andrew Strominger

Abstract

21 pages, no figuresInternational audienceQuantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) 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 c_L=12J / \hbar. 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 T_L=1/2\pi and conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. 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 c_L=12J / \hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L \sim 2 \times 10^{79}

Topics: [PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]
Publisher: HAL CCSD
Year: 2009
DOI identifier: 10.1103/PhysRevD.80.124008
OAI identifier: oai:HAL:hal-00528860v1
Provided by: Hal-Diderot
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