Some remarks on Hayward-AdS black hole surrounded by a fluid of strings

TL;DR

This paper generalizes the Hayward black hole solution by including a cosmological constant and a string fluid, analyzing its regularity, singularities, and thermodynamic properties, with a focus on how these features depend on key parameters.

Contribution

It introduces a new class of solutions extending the Hayward black hole with a string fluid and cosmological constant, examining their regularity and thermodynamics.

Findings

Regularity depends on parameter β, with some solutions preserving the original Hayward black hole's regularity.

Thermodynamic quantities such as pressure, heat capacity, and phase transition points are affected by parameters q and b.

The solution's singularity structure and phase behavior are characterized through curvature invariants and free energy analysis.

Abstract

We obtain a class of solutions corresponding to a generalization of the Hayward black hole by solving the Einstein equations coupled to a particular nonlinear electromagnetic field. The generalization is realized by considering, additionally, the presence of the cosmological constant and a source corresponding to an anisotropic fluid, namely, a fluid of strings, that surrounds the black hole. We show that the obtained class of solutions preserves or does not the regularity of the original Hayward black hole solution, depending on the values of the parameter $\beta$ which labels the different solutions. We discuss the characteristics of the solutions, from the point of view of the singularities of spacetime, by examining the behavior of the Kretschmann scalar as well as of the geodesics concerning their completeness. We analyze some aspects of thermodynamics, particularizing one of the solutions obtained, namely, for $\beta =-1/2$, in which case the regularity of the Hayward black hole is preserved. Some thermodynamic quantities are obtained and analyzed, for example, pressure, heat capacity, and the critical points, and we show how these quantities change for different values of the parameter $q$ associated with the original Hayward solution, as well as with the parameter $b$ associated with the presence of the fluid of strings. The phase transitions are also analyzed by using the equation of state and the Gibbs free energy.