# Thermodynamics of Asymptotically Flat Dyonic Black Holes

## TL;DR

This paper studies the thermodynamics of dyonic black holes with scalar hair in flat spacetime, showing scalar charges do not affect the first law and comparing methods to find exact solutions.

## Contribution

It demonstrates that scalar charges do not contribute to black hole thermodynamics and compares two methods for obtaining exact solutions.

## Key findings

- Scalar charges do not contribute to the first law of thermodynamics.
- Unified approach to deriving exact solutions.
- Detailed analysis of different solution ansatzes.

## Abstract

We investigate the thermodynamics of dyonic hairy black holes in flat spacetime when the asymptotic value of the scalar field is not fixed. We use the quasilocal formalism of Brown and York and corresponding boundary terms that make the variational principle well defined to prove that the scalar charges do not contribute to the first law of thermodynamics. We also provide a unified picture of obtaining exact solutions by comparing two different methods and discuss in detail the ansatz used in each coordinate system and the relation between them.