New Anisotropic Gauss-Bonnet Black Holes in Five Dimensions at the Critical Point

TL;DR

This paper presents new anisotropic black hole solutions in five-dimensional Einstein-Gauss-Bonnet gravity at the critical coupling, revealing unique horizon structures and degeneracies not seen in standard warped product solutions.

Contribution

It introduces novel vacuum static black hole solutions with anisotropic horizons at the critical Gauss-Bonnet coupling, including a uniqueness theorem for certain cases.

Findings

Solutions lack a common warping factor.

Horizon cross section exhibits anisotropy.

Degeneracy in metric functions related to critical coupling.

Abstract

We obtain new vacuum static black hole solutions with anisotropic horizons in Einstein-Gauss-Bonnet gravity with a negative cosmological constant in five dimensions. The translational invariance along one direction on the 3-dimensional horizon cross section is broken. The Gauss-Bonnet coupling {\alpha} is at the critical point where there is one single AdS vacuum. These solutions does not appear in the form of a warped product, i.e. they lack a common warping factor, and the metric contains 2 arbitrary functions, h(r) of the radial coordinate r and H(y) of the horizon coordinate y -- some degeneracy in the metric. The nontrivial horizon and the degeneracy may be closely related to the critical value of {\alpha}. We introduce the process of obtaining the solutions and some of their properties, and also prove a uniqueness theorem for the case when there is a common warping factor for the rest two directions.