Charged dust spheres in the general theory of relativity

Tolman's problem for charged dust is solved in quadratures. The external solution (Reisner-Nordstrom) is obtained in the natural reference frames of charged test particles. The conditions for matching a charged dust sphere with a vacuum over a fixed Lagrangian sphere are formulated. They are equivalent to boundary conditions on the initial data.Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 4, pp. 107–113, April, 1976.The author is deeply grateful to his colleagues K. A. Bronnikov and M. A. Koval'chuk for discussion of this article and a number of valuable remarks.