New regular black hole solutions and other electrically charged compact objects with a de Sitter core and a matter layer

TL;DR

This paper constructs regular black hole and compact object solutions with a de Sitter core by matching an interior nonisotropic charged fluid to an exterior Reissner-Nordström spacetime, using thin shell junction conditions.

Contribution

It introduces a method to generate regular black hole solutions with a de Sitter interior and a matter shell, expanding the class of known charged compact objects in Einstein-Maxwell theory.

Findings

Existence of electrically charged regular black hole solutions.

Identification of conditions for stable matter shells.

Properties of the solutions depend on the shell's equation of state.

Abstract

The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this purpose, we first write explicitly the Einstein field equations for the interior regular region. We take an electrically charged nonisotropic fluid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure $p_r$ is equal to the negative of energy density $\rho$, $p_r=-\rho$. Then, two solutions for the Einstein equations are built, a regular interior solution for the region with matter satisfying a de Sitter equation of state, and an external solution for the region outside the matter, that corresponds to the Reissner-Nordstr\"om metric. To complete the solution we apply the Darmois-Israel junction conditions with a timelike thin shell at the matching surface. It is assumed that the matching surface is composed by a thin shell of matter, i.e., a surface layer in the form a perfect fluid obeying a barotropic equation of state, $\mathcal{P}=\omega\sigma$, $P$ and $\sigma $ being the intrinsic pressure and energy density of the shell, respectively, and $\omega$ a constant parameter. We show that there are electrically charged regular black hole solutions and other compact objects for specific choices of $\omega$ and of the other parameters of the model. Some properties of the objects are investigated.