Algebraic Rainich theory and antisymmetrisation in higher dimensions

Abstract

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.

16 pages, LaTeX

References in corpus (2)

• Dimensionally Dependent Tensor Identities by Double Antisymmetrisation
• Null cone preserving maps, causal tensors and algebraic Rainich theory

Cited by in corpus (8)

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• Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples
• Old and new results for superenergy tensors from dimensionally dependent tensor identities
• Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
• Highly structured tensor identities for (2,2)-forms in four dimensions