Enhanced symmetry and Entropy of Schwarzschild-deSitter spacetime

Abstract

In this paper we show that the equation of motion of a massless scalar particle near the black hole (BH) horizon in the Schwarzschild-deSitter (SdS) spacetime enjoys a hidden conformal symmetry when the two horizons satisfy a quadratic relation, not related with the Nariai limit. This hidden symmetry is $SL(2,\mathbb{R})\times SO(2)$ instead of $SO(2,1)\times SO(2)$, the expected symmetry of $dS_2\times S^2$. We present a structural analysis of SdS spacetime and compute the leading quantum corrections to the entropy of SdS spacetime in a semi-classical way.