The Schwarzschild/CFT Correspondence: Weyl Rescaled Case

Abstract

In this work, the CFT dual of the Schwarzschild black hole is investigated. A Weyl rescaling factor is presented, so that the Weyl rescaled Schwarzschild metric, after a coordinate transformation, has an $AdS_{2} \times S^{2}$ geometry at vicinity of its origin. Since the near origin spacetime admits an $AdS_{2}$ factor, it is dealt with a 2D effective gravity which is dimensionally reduced from the near origin solution. It is exhibited that the dual CFT has a central charge $c=96 M^3$ which is an asymptotic conserved charge of the effective solution. Finally, the microscopic entropy of Schwarzschild black hole is achieved by using Cardy formula. It is revealed that the microscopic entropy exactly reproduces the Bekenstein-Hawking entropy of the Schwarzschild black hole.