Avoidance of singularities in spherically symmetric charged dust

TL;DR

This paper investigates conditions under which singularities can be avoided in spherically symmetric charged dust models, revealing scenarios where the Big Bang/Crunch and shell crossing singularities can be circumvented, allowing passage through a charged dust tunnel.

Contribution

It demonstrates that in charged dust models, singularities can be avoided under specific initial conditions, extending understanding of singularity avoidance in relativistic dust solutions.

Findings

Singularity avoidance depends on charge density relative to mass-energy density.

Certain initial conditions allow the model to avoid both BB/BC and shell crossing singularities.

Charged dust can theoretically pass through a tunnel between singularities in extended spacetime.

Abstract

In spherically symmetric charged dust, just like in electrically neutral dust, two kinds of singularity may be present: the Big Bang/Crunch (BB/BC) singularity, and shell crossings. Quite unlike in neutral dust, the BB/BC singularity may be avoided. When the absolute value of the charge density r is everywhere small compared to the mass-energy density d (|r| < D = \sqrt{G} d / c^2), the conditions that allow the model to avoid the BB/BC singularity necessarily lead to shell crossings. There exist sets of initial conditions that allow us to avoid both singularities (when either |r| > D everywhere, or |r| = D at the center of symmetry while |r| < D elsewhere). In those cases, both kinds of singularity may be avoided for a sufficiently long period that a body of charged dust may go through the tunnel between the singularities in the maximally extended Reissner -- Nordstrom spacetime, to emerge into another asymptotically flat region. An explicit example of such a configuration is presented and discussed. It does not contradict any astrophysical constraints.