The family of regular interiors for non-rotating black holes with $T^0_0 = T^1_1$

TL;DR

This paper derives a general class of solutions for static black hole interiors with a specific stress-energy tensor form, unifying previous models and exploring their energy properties and potential generalizations.

Contribution

It provides the first comprehensive solution family for black hole interiors with $T^0_0 = T^1_1$, encompassing known models and suggesting a framework for including other sources.

Findings

All known solutions are recovered within the general scheme.

Solutions feature a smooth transition from core to exterior.

Discussion on energy properties and potential extensions.

Abstract

We find the general solution for the spacetimes describing the interior of static black holes with an equation of state of the type $ T^0_0 = T^1_1 $ ($T$ being the stress-energy tensor). This form is the one expected from taking into account different quantum effects associated with strong gravitational fields. We recover all the particular examples found in the literature. We remark that all the solutions found follow the natural scheme of an interior core linked smoothly with the exterior solution by a transient region. We also discuss their local energy properties and give the main ideas involved in a possible generalization of the scheme, in order to include other realistic types of sources.