# Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential

## TL;DR

This paper analyzes the thermodynamics of new asymptotically flat hairy black holes with a dilaton potential, demonstrating their stability without artificial boundary conditions, using a counterterm method.

## Contribution

It introduces the first example of thermodynamically stable asymptotically flat black holes with a dilaton potential, analyzed via a counterterm approach.

## Key findings

- Existence of thermodynamically stable black holes in certain parameter ranges.
- Stability shown in both grand canonical and canonical ensembles.
- First demonstration of stable asymptotically flat black holes without artificial boundaries.

## Abstract

We present a detailed analysis of the thermodynamics of exact asymptotically flat hairy black holes in Einstein-Maxwell-dilaton theory. We compute the regularized action, quasilocal stress tensor, and conserved charges by using a `counterterm method' similar to the one extensively used in the AdS-CFT duality. In the presence of a non-trivial dilaton potential that vanishes at the boundary we prove that, for some range of parameters, there exist thermodynamically stable black holes in the grand canonical and canonical ensembles. To the best of our knowledge, this is the first example of a thermodynamically stable asymptotically flat black hole, without imposing artificial conditions corresponding to embedding in a finite box.