Bardeen solution with a cloud of strings

TL;DR

This paper introduces a Bardeen black hole solution surrounded by a string cloud, analyzing its horizon, singularity, and thermodynamic phases, revealing phase transitions and critical behavior similar to Van der Waals fluids.

Contribution

The study extends the Bardeen black hole model by incorporating a string cloud, analyzing its thermodynamics, phase structure, and critical exponents, highlighting new singularity features and phase behavior.

Findings

The solution has the same event horizon as the Bardeen black hole.

The string parameter introduces a singularity at the origin.

The system exhibits three thermodynamic phases with two stable.

Abstract

In this paper we present a Bardeen solution surrounded by a cloud of strings fluid. We show how this model has the same event horizon characteristic as the Bardeen solution, however, the parameter of the strings make the solution singular at the origin. We also analyze the solution from a thermodynamic point of view. We calculate the system's state function, enthalpy; the temperature; and the other potentials; as a function of entropy. By analyzing the thermodynamic coefficients, we show that the solution presents three distinct phases, two of which are stable and one unstable. These three phases could be best visualized using a plot of Gibbs free energy versus temperature. In the end, we calculate the critical exponents and find that they are the same as those found in Van der Walls theory.