Static spherically symmetric black hole's solution in Einstein-Maxwell-Yang-Mills-dilaton theory

TL;DR

This paper derives a static spherically symmetric black hole solution in Einstein-Maxwell-Yang-Mills-dilaton theory, analyzes its singularities, thermodynamics, phase transitions, and critical exponents, revealing complex thermodynamic behavior similar to other dilaton black holes.

Contribution

The paper provides a new black hole solution in Einstein-Maxwell-Yang-Mills-dilaton theory and explores its thermodynamic properties and phase transitions.

Findings

Calculated Kretschmann scalar to identify singularities.

Discovered first and zeroth order phase transitions below critical temperature.

Found critical exponents match those of other dilaton black holes.

Abstract

In this work a static spherically symmetric black hole's solution within the Einstein-Maxwell-Yang-Mills-dilaton theory is derived. The obtained solution is examined, in particular, we have calculated the Kretschmann scalar which allowed us to characterize singularity points. Using the obtained black hole's solution we have studied its thermodynamics. Namely, the temperature was calculated, the first law was written, and the heat capacity was studied. The extended thermodynamics approach is utilized to obtain the equation of state. Within the extended thermodynamics the Gibbs free energy is derived and investigated. The analysis of the Gibbs free energy shows that below the critical temperature besides the first order phase transition in addition the zeroth order phase transition occurs, what is typical for other types of black holes with dilaton fields. Finally, we have shown that the critical exponents take the same values as for other types of the dilaton black holes.