Bardeen solution with a cloud of strings

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, temperature, and 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 is unstable. These three phases could be best visualized using a plot of Gibbs free energy versus temperature. Finally, we calculate the critical exponents and find that they are the same as those found in Van der Walls theory.

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