Thermodynamics of regular black hole interiors

Abstract

A regular black hole is represented by a singularity-free solution of the Einstein's field equations. One possible set of regular black hole solutions has the geometry of the space-time described by Schwarschild's solution at large radii and by a de Sitter-like solution at small radii. Solutions of this kind can be found for some choices of the equation of state in a static, spherically symmetric configuration. Adopting the equation of state suggested by Mbonye and Kanzanas (2005), the model of the interior of the black hole consists of matter fields with sound speed bounded by the speed of light. The matter transits smoothly between normal matter and a core of a "quintessence-like" fluid with an equation of state that approaches p = −rho when r -> 0. In this work we address the question of the thermodynamical behavior of the matter that constitutes the interior of this non-singular black hole model. We derive the general equations of the thermodynamic quantities for an arbitrary density profile and adjust the results to the specific regular black hole. Then, we discuss a possible physical interpretation of the state of regular black hole interiors.