Can a charged dust ball be sent through the Reissner--Nordstr\"{o}m wormhole?

TL;DR

This paper investigates the properties of charged dust in Reissner--Nordström wormholes, revealing the inevitability of singularities with infinite and direction-dependent energy densities, and explores conditions for pulsating configurations.

Contribution

It provides new insights into the energy density behavior and singularities in charged dust wormholes, extending previous conditions for avoiding collapse.

Findings

Existence of a point singularity with infinite energy density.

Direction-dependent divergence of energy density at the singularity.

Pulsating configurations require a permanent central singularity.

Abstract

In a previous paper we formulated a set of necessary conditions for the spherically symmetric weakly charged dust to avoid Big Bang/Big Crunch, shell crossing and permanent central singularities. However, we did not discuss the properties of the energy density, some of which are surprising and seem not to have been known up to now. A singularity of infinite energy density does exist -- it is a point singularity situated on the world line of the center of symmetry. The condition that no mass shell collapses to $R = 0$ if it had $R > 0$ initially thus turns out to be still insufficient for avoiding a singularity. Moreover, at the singularity the energy density $\epsilon$ is direction-dependent: $\epsilon \to - \infty$ when we approach the singular point along a $t =$ const hypersurface and $\epsilon \to + \infty$ when we approach that point along the center of symmetry. The appearance of negative-energy-density regions turns out to be inevitable. We discuss various aspects of this property of our configuration. We also show that a permanently pulsating configuration, with the period of pulsation independent of mass, is possible only if there exists a permanent central singularity.