Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
2005 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 461, no 2059, 2181-2195 p.Article in journal (Refereed) Published
We present a study of 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 gain 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.
Place, publisher, year, edition, pages
2005. Vol. 461, no 2059, 2181-2195 p.
IdentifiersURN: urn:nbn:se:liu:diva-22453DOI: 10.1098/rspa.2004.1411Local ID: 1676OAI: oai:DiVA.org:liu-22453DiVA: diva2:242766