A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

Statistics – Computation

Scientific paper

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Computational Astrophysics, Einstein Equations, Space-Time Functions, Black Holes (Astronomy), Laplace Equation, Maxwell Equation, Vacuum

Scientific paper

A one-to-one correspondence is established between the static solutions of the Einstein-Maxwell equations and the stationary solutions of the Einstein-vacuum equations, that enables one to directly write down a solution for the one from a known solution of the other, and conversely, by a simple transcription. The directness of the correspondence is achieved by writing the metric for static Einstein-Maxwell space-times in a coordinate system and a gauge adapted to the two-center problem and the metric for stationary Einstein-vacuum space-times in a coordinate system and a gauge adapted to black holes with event horizons.

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