Gauss-Bonnet Black Holes in dS Spaces

TL;DR

This paper investigates the thermodynamic stability of Gauss-Bonnet black holes in de Sitter space, revealing dimension-dependent stability properties and constraints on black hole size related to the Gauss-Bonnet coefficient.

Contribution

It provides a detailed analysis of the thermodynamic behavior of Gauss-Bonnet black holes in dS spaces, including stability conditions and bounds on horizon sizes based on the Gauss-Bonnet coefficient.

Findings

Small black holes are locally stable in 5D with positive Gauss-Bonnet coefficient.

Black holes are always thermodynamically unstable in higher dimensions for positive coefficient.

Pure de Sitter space is globally preferred and stable across scenarios.

Abstract

We study the thermodynamic properties associated with black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension $d=5$, the stable small black hole disappears and the Gauss-Bonnet black hole is always unstable quantum mechanically when $d \ge 6$. On the other hand, the cosmological horizon is found always locally stable independent of the spacetime dimension. But the solution is not globally preferred, instead the pure de Sitter space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on the value of the coefficient, beyond which the gravity theory is not well defined. As a result, there is not only an upper bound on the size of black hole horizon radius at which the black hole horizon and cosmological horizon coincide with each other, but also a lower bound depending on the Gauss-Bonnet coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable and the cosmological horizon is always stable, further, as the case of the positive coefficient, the pure de Sitter space is still globally preferred. This result is consistent with the argument that the pure de Sitter space corresponds to an UV fixed point of dual field theory.