Frolov Black Hole Surrounded by a Cloud of Strings

TL;DR

This work extends the Frolov regular black hole by embedding it in a cloud of strings described by a Letelier source, deriving the modified metric and analyzing its curvature, geodesics, energy conditions, and thermodynamics. They find that the cloud-induced modification yields a curvature singularity at the origin (K → ∞ as r → 0) despite geodesic completeness for certain energy conditions, and they show how the cloud parameter a and scale l shift thermodynamic quantities such as the mass–entropy relation, Hawking temperature T(S), and heat capacity C(S). The paper clarifies the tension between curvature regularity and geodesic completeness in spacetimes with a string cloud and highlights how the cloud alters stability and phase transitions relative to the original Frolov solution. These results contribute to understanding regular black holes with exotic matter sources and their thermodynamic behavior in modified gravity contexts, including connections to Hayward and RN benchmarks.

Abstract

We obtain the metric which describes the spacetime corresponding to the Frolov black hole in the presence of a cloud of strings and discuss how this cloud affects the regularity of the solution and the energy conditions. In addition, we analyze geodesics, effective potential, and several thermodynamic aspects. Finally, we compare our results with the corresponding findings in the literature for the original Frolov black hole, that is, in the absence of a cloud of strings

Figures (4)

• Figure 1: The left plot shows $\dot{r}^2$ for $E=2$. The right plot shows the effective potential $V_{eff} = f(r)$.
• Figure 2: Black hole mass as a function of entropy $m(S)$ for different values of $a$, $Q$ and $l$.
• Figure 3: Black hole temperature as a function of entropy $T(S)$ for different values of $a$, $Q$ and $l$.
• Figure 4: Heat capacity as a function of entropy $C(S)$ for different values of $a$, $Q$ and $l$.