The RN/CFT correspondence

Recently it has been shown in [S.M. Carroll, et al., arXiv:0901.0931 [hep-th]] that the approach to extremality for the non-extremal Reissner-Nordstrom black hole is not continuous. The non-extremal RN black hole splits into two spacetimes at the extremality: an extremal black hole and a disconnected AdS2×S2 space which has been called the “compactification solution”. As a possible resolution for understanding the entropy of extremal RN black hole, it has been speculated that the entropy of the non-extremal black hole may be carried by the latter solution. By uplifting the four-dimensional “compactification solution” with electric charge Qe to a five-dimensional solution, we show that this solution is dual to a CFT with central charge c=6Qe3. The Cardy formula then shows that the microscopic entropy of the CFT is the same as the macroscopic entropy of the “compactification solution”.