The Kerr/CFT Correspondence

Monica Guica UniversitĀ“e Pierre et Marie Curie-Paris 6 Thomas Hartman Harvard University Wei Song Harvard University Andrew Strominger Harvard University

Mathematical Physics mathscidoc:1702.22035

Physical Review D Particles & Fields, 80, (12), 2008.3
Quantum 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}.
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@inproceedings{monica2008the,
  title={The Kerr/CFT Correspondence},
  author={Monica Guica, Thomas Hartman, Wei Song, and Andrew Strominger},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228114226311333559},
  booktitle={Physical Review D Particles & Fields},
  volume={80},
  number={12},
  year={2008},
}
Monica Guica, Thomas Hartman, Wei Song, and Andrew Strominger. The Kerr/CFT Correspondence. 2008. Vol. 80. In Physical Review D Particles & Fields. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228114226311333559.
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