# Slowly rotating Einstein-Maxwell-dilaton black hole and some aspects of its thermodynamics

## TL;DR

This paper explores the thermodynamics of a slowly rotating Einstein-Maxwell-dilaton black hole, revealing phase transitions, critical behavior, and thermodynamic properties using extended techniques and Van der Waals analogy.

## Contribution

It presents a new analysis of thermodynamic phase transitions and critical phenomena in Einstein-Maxwell-dilaton black holes, including phase coexistence and latent heat calculations.

## Key findings

- Black hole exhibits first and zeroth order phase transitions below a critical temperature.
- Equation of state resembles Van der Waals fluid with critical exponents calculated.
- Thermodynamic functions such as temperature, entropy, and heat capacity are analyzed.

## Abstract

A slowly rotating black hole solution in Einstein-Maxwell-dilaton gravity was considered. Having used the obtained solution we investigated thermodynamic functions such as black hole's temperature, entropy and heat capacity. In addition to examine thermodynamic properties of the black hole extended technique was applied. The equation of state of Van der Waals type was obtained and investigated. It has been shown that the given system has phase transitions of the first as well as of the zeroth order for the temperatures below a critical one which is notable feature of the black hole. A coexistence relation for two phases was also considered and latent heat was calculated. In the end, critical exponents were calculated.