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The Spacetime Geometry of a Null Electromagnetic Field · Around

2013

The Spacetime Geometry of a Null Electromagnetic Field

Torre, C. G.

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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.

Built on

G. Y. Rainich, Trans. Am. Math. Soc
1925
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L. Mariot, C. R. Acad. Sci. (Paris)
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C. Misner and J. Wheeler, Ann. Phys
1957
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I. Robinson, J. Math. Phys
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Earlier work this paper cites.

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J. Stewart, Advanced General Relativity
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P. Nurowski and J. Tafel, Class. Quantum Grav
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Then

S. Lang, Differential and Riemannian Manifolds
1995
Later among the works it cites.
H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of Einstein’s Field Equations, Second Edition
2003
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I. M. Anderson and C. G. Torre, J. Math. Phys
2012
Later among the works it cites.
C. G. Torre, Class. Quantum Grav
2012
Later among the works it cites.

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