Black holes in Einstein-Gauss-Bonnet gravity with a string cloud background

TL;DR

This paper derives a five-dimensional black hole solution in Einstein-Gauss-Bonnet gravity with a string cloud, analyzing its thermodynamics, stability, and evaporation properties, revealing stable small black holes and phase transitions.

Contribution

It presents a novel black hole solution in Einstein-Gauss-Bonnet gravity with a string cloud and explores its thermodynamic and dynamical stability properties.

Findings

Existence of stable small black holes with specific parameter ranges.

Hawking-Page phase transition identified in the model.

Black hole evaporation times depend on parameters, with some cases having finite evaporation time.

Abstract

We obtain a black hole solution in the Einstein-Gauss-Bonnet theory for the string cloud model in a five dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature $T_{\mathrm{H}}$, the specific heat $C$, the entropy $S$, and the Helmholtz free energy $F$ of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source. We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking-Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss-Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background.