  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.

General Relativity and Quantum Cosmology