Gauss-Bonnet black holes with non-constant curvature horizons

TL;DR

This paper explores higher-dimensional Gauss-Bonnet black holes with non-constant curvature horizons, analyzing their properties, uniqueness, thermodynamics, and stability, extending previous work on constant curvature horizons.

Contribution

It generalizes the understanding of Gauss-Bonnet black holes to non-constant curvature horizons, establishing uniqueness, thermodynamic laws, and stability conditions.

Findings

Most properties of the quasi-local mass mirror constant curvature cases.

The Dotti-Gleiser solution is unique for non-constant warp factors.

Black holes are thermodynamically unstable in certain curvature and cosmological constant regimes.

Abstract

We investigate static and dynamical n(\ge 6)-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an (n-2)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasi-local mass that satisfies the unified first law, we show that most of the properties of the quasi-local mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein space is non-constant. The quasi-local mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the non-zero cosmological constant, it cannot be globally stable for the positive cosmological constant.