(Anti-) de Sitter Black Holes in higher derivative gravity and dual Conformal Field Theories

TL;DR

This paper analyzes the thermodynamics of higher derivative gravity black holes in Anti-de Sitter space, exploring their stability, dual conformal field theories, and universal entropy relations.

Contribution

It provides new insights into black hole thermodynamics in higher derivative gravity and the dual CFT properties, including the Cardy-Verlinde formula in a universal form.

Findings

Black hole entropy can be zero or negative in certain parameter regions.

Black hole solutions are unstable when entropy is zero or negative.

The dual CFT has zero Casimir energy when black hole entropy is zero.

Abstract

Thermodynamics of five-dimensional Schwarzschild Anti-de Sitter (SAdS) and SdS black holes in the particular model of higher derivative gravity is considered. The free energy, mass (thermodynamical energy) and entropy are evaluated. There exists the parameters region where BH entropy is zero or negative. The arguments are given that corresponding BH solutions are not stable. We also present the FRW-equations of motion of time (space)-like branes in SAdS or SdS BH background. The properties of dual CFT are discussed and it is shown that it has zero Casimir energy when BH entropy (effective gravitational constant) is zero. The Cardy-Verlinde formula for CFT dual to SAdS or SdS BH is found in the universal form.