Metric of a~closed Friedman world perturbed by an~electric charge.

M. A. Markov ; V. P. Frolov

Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 3-17

Résumé

Tolmans' well-know problem is generalized to the case of electrically ctmrged dust-like matter of a centrally symmetric system. First integrals are found of the corresponding Einstein–Maxwell equations. The problem is then specialized in such a way that the metric of a closed Friedman world ts obtained when the total charge of the system tends to zero. Such a system is considered at the initial instant, the time of maxlmum expansion. For any arbitrarily small electric charge, the metric is not ctosed. The metric of the almost Friedman part of the world is continued through a narrow throat (for a small charge) by the Nordström–Reissner metric with parameters satisfying $\sqrt{\varkappa} m_0=e_0$. The expression for the electric potential in the throat $\varphi_h=c^2/\sqrt{\varkappa}$ does not depend on the magnitude of the electric charge. With increasing charge, the radius of the throat increases ($r_h=e_0\sqrt{\varkappa}/c^2$). The state of the throat in the classical description is essentially unstable from the point of view of quantum physics. The generation of all kinds of pairs in the tremendously strong electric fields of the throat polarize the latter to an effective charge $Z137e$, irrespective of the initial, arbitrarily large charge of the material system.