Black plane solutions in four dimensional spacetimes

TL;DR

The work analyzes static plane- and cylindrical-symmetric black hole solutions in four-dimensional Einstein-Maxwell theory with a negative cosmological constant $\Lambda = -3\alpha^2$, deriving RN-like horizons for black membranes and strings and establishing their thermodynamics, including a Hawking temperature that scales as $M^{1/3}$ in the neutral case. It also extends the analysis to Einstein-Maxwell-dilaton gravity with a Liouville potential, showing that the dilaton field radically changes horizon structures and asymptotics, yielding AdS or dS behavior depending on parameters. The paper demonstrates Vaidya-like time-dependent generalizations and discusses inner-horizon instabilities, deepening the understanding of black brane solutions in AdS contexts. Overall, it broadens the catalog of exact AdS black p-brane solutions and clarifies how dilaton couplings modify their geometry and thermodynamics.

Abstract

The static, plane symmetric solutions and cylindrically symmetric solutions of Einstein-Maxwell equations with a negative cosmological constant are investigated. These black configurations are asymptotically anti-de Sitter not only in the transverse directions, but also in the membrane or string directions. Their causal structure is similar to that of Reissner-Nordström black holes, but their Hawking temperature goes with $M^{1/3}$, where $M$ is the ADM mass density. We also discuss the static plane solutions in Einstein-Maxwell-dilaton gravity with a Liouville-type dilaton potential. The presence of the dilaton field changes drastically the structure of solutions. They are asymptotically ``anti-de Sitter'' or ``de Sitter'' depending on the parameters in the theory.