Intermediate scalings for solv, nil, and SL2 (R) black branes

Abstract

In this work, we will study black brane solutions that are not translationally invariant in the spatial directions along which it extends. Instead, we require homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. We find Einstein-Maxwell-anti-de Sitter black hole solutions of which the near-horizon geometry corresponds to solv (Bianchi V1-1), nil (Bianchi II), or SL2(R) (Bianchi VIII). Interestingly, we observe that at intermediate temperatures our solutions have an scaling regime where different spacetime directions scale differently. We also compute the dc conductivities for these charged solutions and study how they scale in this intermediate regime.