# The Kerr/CFT Correspondence

 Title: The Kerr/CFT Correspondence Author: Guica, Monica; Hartman, Thomas; Strominger, Andrew E.; Song, Wei Note: Order does not necessarily reflect citation order of authors. Citation: Guica, Monica, Thomas Hartman, Wei Song, and Andrew E. Strominger. 2009. The Kerr/CFT correspondence. Physical Review D 80(12): 124008. Full Text & Related Files: 0809.4266v1.pdf (252.6Kb; PDF) Abstract: Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by $$J = GM^2$$) 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 $$c_L\sim 2 \times 10^{79}$$. Published Version: doi:10.1103/PhysRevD.80.124008 Other Sources: http://arxiv.org/abs/0809.4266 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8156576 Downloads of this work: