Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-02-26
Class.Quant.Grav. 19 (2002) 3341-3356
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages, LaTeX
Scientific paper
10.1088/0264-9381/19/12/316
The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor $T$ to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations these conditions can be expressed in terms of the Ricci tensor, thus providing conditions on a spacetime geometry for it to be an Einstein-Maxwell spacetime. One of the conditions is that $T^2$ is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple $p$-form. Here we examine algebraic Rainich conditions for general $p$-forms in higher dimensions and their relations to identities by antisymmetrisation. Using antisymmetrisation techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse; that the identities are sufficient to determine the form. As an example we obtain the complete generalisation of the classical Rainich theory to five dimensions.
Bergqvist Göran
Hoglund Anders
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