# Exact dynamical black hole solutions in five or higher dimensions

## TL;DR

The paper presents new black hole solutions in higher dimensions with a dilaton field and varying cosmological constants.

## Contribution

The novelty is constructing non-stationary black hole solutions with arbitrary coupling constants in higher-dimensional Einstein–Maxwell theory.

## Key findings

- Three distinct classes of solutions are found based on coupling constants.
- Solutions can be asymptotically de-Sitter, anti-de-Sitter, or flat.
- The solutions are non-stationary and conformally regular.

## 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 an 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.