Classical and Quantum Gravity
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a nullelectromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given aspacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the nullelectromagnetic field from the metric. Null electrovacuum geometry is illustrated using some pure radiation spacetimes taken from the literature.
C G Torre. (2014). The spacetime geometry of a null electromagnetic field. Classical and Quantum Gravity, 31(4), 045022.