6 Avoidance of singularities in spherically symmetric charged dust

In spherically symmetric charged dust, just like in 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 charge density ρe and the mass-energy density ǫ obey |ρe| < De def = √ Gǫ/c2, the conditions that allow the model to avoid the BB/BC singularity necessarily lead to shell crossings. However, when |ρe| → De at the center of symmetry while |ρe| < De 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 – Nordström 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. 1 Spherically symmetric dust in electromagnetic field For the spherically symmetric spacetimes in the comoving coordinates, the metric can be put in the form ds = edt − edr − R(t, r) [ dθ + sin(θ)dφ ] . (1.1) The case R,r = 0 requires separate consideration. In this case, a solution of the Einstein equations for electrically neutral dust was found by Datt [1] and then derived and interpreted by Ruban [2, 3]; the corresponding Einstein–Maxwell equations were systematically derived and solved by Ruban [4, 5, 6]. We will discuss the solutions of the Einstein–Maxwell equations in the generic case R,r 6= 0. Most of the material of Sections 2 to 7 has been known for a long time, but a few points were overlooked by some of the earlier authors. That material is reviewed here in order to introduce the framework and notation, and to fill in the few little gaps. New results are reported in Sections 8 and following. ∗This research was supported by the Polish Ministry of Education and Science grant no 1 P03B 075 29.