Proofs of existence of local potentials for trace-free symmetric 2-forms using dimensionally dependent identities

S. Brian Edgar

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arXiv · gr-qc/0407002

Proofs of existence of local potentials for trace-free symmetric 2-forms using dimensionally dependent identities

S. Brian Edgar

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Abstract

We exploit four-dimensional tensor identities to give a very simple proof of the existence of a Lanczos potential for a Weyl tensor in four dimensions with any signature, and to show that the potential satisfies a simple linear second order differential equation, e.g., a wave equation in Lorentz signature. Furthermore, we exploit higher dimensional tensor identities to obtain the analogous results for (m,m)-forms in 2m dimensions.

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S. Brian Edgar. 2004-07-01. Proofs of existence of local potentials for trace-free symmetric 2-forms using dimensionally dependent identities. https://arxiv.org/abs/gr-qc/0407002

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