The RN/CFT Correspondence

TL;DR

This paper demonstrates that the compactification solution of the non-extremal Reissner-Nordstrom black hole is dual to a conformal field theory, providing a microscopic explanation for its entropy through the Cardy formula.

Contribution

It establishes a duality between the uplifted compactification solution and a CFT with a specific central charge, linking microscopic and macroscopic entropy calculations.

Findings

The uplifted solution is dual to a CFT with central charge c=6Q_e^3.

The Cardy formula reproduces the entropy of the compactification solution.

The approach clarifies the entropy origin of non-extremal RN black holes.

Abstract

Recently it has been shown in 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 $AdS_2\times S^2$ 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 $Q_e$ to a five dimensional solution, we show that this solution is dual to a CFT with central charge $c=6Q_e^3$. The Cardy formula then shows that the microscopic entropy of the CFT is the same as the macroscopic entropy of the "compactification solution".