New anisotropic Gauss–Bonnet black holes in five dimensions at the critical point

Abstract

AbstractWe 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 $$\alpha $$ α 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 $$\alpha $$ α . 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.