Black plane solutions in four dimensional spacetimes

TL;DR

This paper explores static black plane and cylindrical solutions in Einstein-Maxwell and Einstein-Maxwell-dilaton theories with negative cosmological constant, revealing their unique causal structures and asymptotic behaviors.

Contribution

It introduces new static black plane solutions in four-dimensional spacetimes, analyzing their properties and effects of dilaton fields on their structure.

Findings

Black plane solutions are asymptotically anti-de Sitter in multiple directions.

Their Hawking temperature scales with the cube root of mass density.

Dilaton fields significantly alter the solution structures, leading to diverse asymptotic behaviors.

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-Nordstr\"{o}m 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.