Avoidance of singularities in spherically symmetric charged dust

Abstract

In spherically symmetric charged dust, just like in neutral dust, two kinds of singularity may be present: the big bang/big crunch (BB/BC) singularity, and shell crossings. Quite unlike in neutral dust, the BB/BC singularity may be avoided. When the charge density ${\ensuremath{\rho}}_{e}$ and the mass-energy density $ϵ$ obey $|{\ensuremath{\rho}}_{e}|<\phantom{\rule{0ex}{0ex}}{D}_{e}\stackrel{\mathrm{def}}{=}\sqrt{G}ϵ/{c}^{2}$, the conditions that allow the model to avoid the BB/BC singularity necessarily lead to shell crossings. However, when $|{\ensuremath{\rho}}_{e}|\ensuremath{\rightarrow}{D}_{e}$ at the center of symmetry while $|{\ensuremath{\rho}}_{e}|<{D}_{e}$ elsewhere, 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-Nordstr\"om 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.