Regular and quasi black hole solutions for spherically symmetric charged dust distributions in the Einstein-Maxwell theory

TL;DR

This paper investigates static, spherically symmetric charged dust solutions in Einstein-Maxwell theory, revealing bifurcations where solutions can resemble either flat spacetime or black holes, depending on source strength.

Contribution

It presents a unified analysis of regular and quasi black hole solutions for charged dust in Einstein-Maxwell theory, uncovering bifurcation phenomena.

Findings

Bifurcation behavior in solutions based on source strength

Existence of solutions approaching Minkowski spacetime

Solutions approaching black hole configurations

Abstract

Static spherically symmetric distributions of electrically counterpoised dust (ECD) are used to construct solutions to Einstein-Maxwell equations in Majumdar--Papapetrou formalism. Unexpected bifurcating behaviour of solutions with regard to source strength is found for localized, as well as for the delta-function ECD distributions. Unified treatment of general ECD distributions is accomplished and it is shown that for certain source strengths one class of regular solutions approaches Minkowski spacetime, while the other comes arbitrarily close to black hole solutions.