Some remarks on Frolov-AdS black hole surrounded by a fluid of string

TL;DR

This paper introduces new solutions extending the Frolov-AdS black hole by incorporating a cosmological constant and a string fluid, analyzing their regularity, singularities, geodesic completeness, and thermodynamic properties.

Contribution

It presents a generalized class of solutions that maintain regularity under certain parameters, expanding understanding of black hole behavior with string fluids and cosmological constants.

Findings

Some solutions preserve the original regularity of Frolov black holes.

The presence of a string fluid affects singularity and geodesic completeness.

Thermodynamic analysis reveals parameter-dependent behaviors.

Abstract

A class of new solutions that generalizes the Frolov regular black hole solution is obtained. The generalization is performed by adding the cosmological constant and surrounding the black hole with a fluid of strings. Among these solutions, some preserve the regularity of the original Frolov solution, depending on the values of the parameter $\beta$, which labels the different solutions. A discussion is presented on the features of the solutions with respect to the existence or not of singularities, by examining the Kretschmann scalar, as well as by analysing the behavior of the geodesics concerning their completeness. It is performed some investigations concerning different aspects of thermodynamics, concerning the role played by the parameter associated with the Frolov regular black hole solution, as well as the parameter that codifies the presence of the fluid of strings. These are realized by considering different values of the parameter $\beta$, in particular, for $\beta=- 1/2$, in which case the regularity of the Frolov black hole is preserved. All obtained results closely align with the ones obtained by taking the appropriate particularizations.