Person:

Song, Wei

Three dimensional Einstein gravity with negative cosmological constant (-1/\ell^2) deformed by a gravitational Chern-Simons action with coefficient (1/\mu) is studied in an asymptotically (AdS_3) spacetime. It is argued to violate unitary or positivity for generic (\mu) due to negative-energy massive gravitons. However at the critical value (\mu\ell=1), the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by (\ell M=J). The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges ((c_L,c_R)=(0,3\ell /G)).

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}).