Black holes, black strings and cosmological constant

TL;DR

This paper reviews black hole and black string solutions in higher-dimensional Einstein and Einstein-Maxwell theories with a cosmological constant, highlighting their stability, non-uniformity, and effects of Gauss-Bonnet corrections.

Contribution

It provides a comprehensive review of solutions, including new insights into stability, non-uniform black strings, and the impact of Gauss-Bonnet terms in higher dimensions.

Findings

Numerical solutions are necessary due to the cosmological constant.

Non-uniform black strings depend non-trivially on co-dimension.

Gauss-Bonnet term influences the domain of black string existence.

Abstract

We present a review of black holes and black string solutions available in the $d$-dimensional Einstein and Einstein-Maxwell model in the presence of a cosmological constant. Due to the cosmological constant, the equations do not admit explicit solutions for generic values of the parameters and numerical methods are necessary to construct the solutions. Several new features of the solutions are discussed, namely their stability and the occurrence of non-uniform black strings which depend non-trivially on the co-dimension. Black string solutions are further constructed for the Einstein-Gauss-Bonnet model. The influence of the Gauss-Bonnet term on the domain of existence of the black strings is discussed in details.