Constructing regular black holes from multi-polytropic equations of state

TL;DR

This paper constructs new regular black hole solutions using multi-polytropic equations of state within Einstein's equations, avoiding non-linear electrodynamics, and explores their properties, including potential dark energy behavior and thermodynamic interpretations.

Contribution

It introduces a novel method to obtain regular black holes from multipolytropic equations of state satisfying TOV equations without non-linear electrodynamics.

Findings

Regular black holes can exhibit repulsive gravity effects.

Black hole remnants may act as dark energy sources.

Transitions to regular relativistic compact objects are possible.

Abstract

Regular black holes are imagined as solutions to Einstein's field equations, with no singularities, albeit characterized by the presence of an internal structure. With the intention not to use non-linear electrodynamics, we here propose to obtain new classes of solutions that can also satisfy the Tolman-Oppenheimer-Volkoff (TOV) equations, plus adding a non-zero core. Thus, we present regular black holes as solutions to the TOV equations using multipolytropic equations of state and investigate whether these solutions behave, tuning the underlying free parameters. Our analysis demonstrates that, within specific parameter ranges, repulsive gravity effects may occur in precise regions. Accordingly, black hole remnants are also investigated, showing that, under certain circumstances, they may turn into dark energy sources in view of the corresponding repulsive gravity effects, located outside the horizons. Moreover, quite remarkably, critical sets of parameters imply that solutions may exhibit transitions to regular repulsive relativistic compact objects from black hole behaviors. Finally, we explore the interpretation of these regular black hole solutions in terms of topological thermodynamic defects.