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Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank

G. Bergqvist·P. Lankinen
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Abstract

We study Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to obtain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin 3/2 field satisfying the source free field equation.

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G. Bergqvist, P. Lankinen. 2004-09-20. Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank. https://doi.org/10.1098/rspa.2004.1411

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