Exact Dynamical Black Hole Solutions in Five or Higher Dimensions

TL;DR

This paper presents new exact dynamical black hole solutions in higher-dimensional Einstein-Maxwell-dilaton theories with arbitrary cosmological constants, using Bianchi type IX geometry, and analyzes their properties and asymptotic behaviors.

Contribution

It introduces three classes of non-stationary black hole solutions in higher dimensions with non-trivial dilaton interactions and arbitrary cosmological constants, expanding the known solution space.

Findings

Solutions can be asymptotically de-Sitter, anti-de-Sitter, or flat.

Solutions are non-stationary and almost conformally regular.

Different classes depend on coupling constants values.

Abstract

We construct new classes of the dynamical black hole solutions in five or higher dimensional Einstein-Maxwell theory, coupled to a dilaton field, in the presence of arbitrary cosmological constant. The dilaton field interacts non-trivially with the Maxwell field, as well as the cosmological constant, with two arbitrary coupling constants. The solutions are non-stationary, and almost conformally regular everywhere. To construct the solutions, we use the four-dimensional Bianchi type IX geometry, as the base space. We find three different classes of solutions, based on the values of the coupling constants. We notice that our solutions could be asymptotically de-Sitter, anti-de-Sitter or flat. We find the relevant quantities of the solutions, and discuss the properties of the solutions.