Document Type
Article
Publication Date
7-2013
Abstract
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 null electromagnetic 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 a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from the metric. Null electrovacuum geometry is illustrated using some pure radiation spacetimes taken from the literature.
Recommended Citation
Torre, Charles G., "The Spacetime Geometry of a Null Electromagnetic Field" (2013). Presentations and Publications. Paper 5.
https://digitalcommons.usu.edu/dg_pres/5
Included in
Cosmology, Relativity, and Gravity Commons, Elementary Particles and Fields and String Theory Commons, Geometry and Topology Commons
Comments
The bulk of the results were obtained using DifferentialGeometry. This work was supported by grant OCI-1148331 from the National Science Foundation.