Axially symmetric stationary electrovac solutions
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Perjes and Israel and Wilson have given independently a new class of solutions of the sourcefree Einstein-Maxwell equations, which can be interpreted as the external gravitational and electromagnetic fields of a spinning source with unit specific charge. Starting from Zipoy's solutions in oblate and prolate spheroidal coordinates for the source-free gravitational field we generate some axially symmetric stationary solutions of the source-free Einstein-Maxwell equations by using Perjes' method. All these solutions become Euclidean at infinity. The asymptotic behavior and the singularity of the solutions are studied in order to gain some insight into the nature of the source. The solution in prolate spheroidal coordinates is found to contain closed timelike lines.
KeywordsAsymptotic Behavior Electromagnetic Field Stationary Solution Differential Geometry Gravitational Field
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