Mathematics
Scientific paper
Sep 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983gregr..15..823b&link_type=abstract
General Relativity and Gravitation (ISSN 0001-7701), vol. 15, Sept. 1983, p. 823-836.
Mathematics
3
Astronomical Models, Einstein Equations, Gravitational Collapse, Maxwell Equation, Relativity, Singularity (Mathematics), Charged Particles, Cosmic Dust, Field Theory (Physics), Mass Distribution, Quadratures, Space-Time Functions, Symmetry
Scientific paper
For charged dust distributions with spherical, planar, and pseudospherical symmetries the general solution to the Einstein-Maxwell equations is presented in quadratures. For zero cosmological constant all the concrete models are listed. Necessary and sufficient conditions are given for these models to have no temporal (occurring at a certain moment of proper time) singularities. Properties of planarly symmetric configurations are discussed in more detail. In particular, conditions are formulated for a plane layer to be mirror-symmetric in the thickness direction; it is shown that an external electromagnetic field cannot prevent a neutral matter distribution from evolving to a singularity; it is demonstrated that one of two electrovacuum space-times matched to a physically acceptable plane layer of matter can have a Cauchy horizon while the other has none. Examples of regular mirror-symmetric layers are presented.
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