Black hole thermodynamics from logotropic fluids

TL;DR

This paper demonstrates that black hole solutions in Einstein's equations with a negative cosmological constant can exhibit thermodynamics similar to logotropic fluids, linking cosmological fluid models with black hole physics.

Contribution

It introduces a method to derive asymptotic anti-de Sitter black hole solutions that replicate the thermodynamic behavior of logotropic and Anton-Schmidt fluids, expanding the understanding of their gravitational and thermodynamic properties.

Findings

Black hole thermodynamics can match logotropic fluid behavior.

Constructed spacetime functions satisfying energy conditions.

Explored optical properties and effective refractive index variations.

Abstract

We show that the Einstein field equations with a negative cosmological constant can admit black hole solutions whose thermodynamics coincides with that of logotropic fluids, recently investigated to heal some cosmological and astrophysical issues. For this purpose, we adopt the Anton-Schmidt equation of state, which represents a generalized version of logotropic fluids. We thus propose a general treatment to obtain an asymptotic anti-de Sitter metric, reproducing the thermodynamic properties of both Anton-Schmidt and logotropic fluids. Hence, we explore how to construct suitable spacetime functions, invoking an event horizon and fulfilling the null, weak, strong and dominant energy conditions. We further relax the strong energy condition to search for possible additional solutions. Finally, we discuss the optical properties related to a specific class of metrics and show how to construct an effective refractive index depending on the spacetime functions and the thermodynamic quantities of the fluid under study. We also explore possible departures with respect to the case without the fluid.