# Charged dilaton black hole with multiple Liouville potentials and gauge fields

## TL;DR

This paper presents an exact solution in Einstein--Maxwell--dilaton theory with multiple potentials and gauge fields, revealing thermodynamic behaviors similar to Lifshitz black holes and potential phase transitions.

## Contribution

It introduces a new exact solution with arbitrary numbers of Liouville potentials and gauge fields, bridging Lifshitz and topological dilaton black holes.

## Key findings

- Thermodynamic behavior resembles Lifshitz black holes
- Phase transition possible at small charge or potential
- Solution interpolates between different black hole types

## Abstract

A solution to an Einstein--Maxwell--dilaton-type theory with $M$ Liouville potentials and $N$ gauge fields is presented, where $M$ and $N$ are arbitrary integers. This exact solution interpolates between the Lifshitz black hole and the topological dilaton black hole. The thermodynamic behaviour of the solution is found to be similar to that of the Lifshitz black hole, where a phase transition may occur for sufficiently small charge in the canonical ensemble, or sufficiently small potential in the grand canonical ensemble.