Rainich Conditions
In 1925, George Yuri Rainich presented purely mathematical conditions which are both necessary and sufficient for a Lorentzian manifold to admit an interpretation in general relativity as a non-null electrovacuum. These comprise three algebraic conditions and one differential condition. The conditions are sometimes useful for checking that a putative non-null electrovacuum really is what it claims, or even for finding such solutions.
No analogous necessary and sufficient conditions for a null electrovacuum are yet known, although some progress has been made.
Read more about this topic: Electrovacuum Solution
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