Black holes, black strings and cosmological constant

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.