paper

(Super)^n-Energy for arbitrary fields and its interchange: Conserved quantities

arXiv:gr-qc/9905057 · doi:10.1142/S0217732300000153

Abstract

Inspired by classical work of Bel and Robinson, a natural purely algebraic construction of super-energy tensors for arbitrary fields is presented, having good mathematical and physical properties. Remarkably, there appear quantities with mathematical characteristics of energy densities satisfying the dominant property, which provides super-energy estimates useful for global results and helpful in other matters. For physical fields, higher order (super)^n-energy tensors involving the field and its derivatives arise. In Special Relativity, they provide infinitely many conserved quantities. The interchange of super-energy between different fields is shown. The discontinuity propagation law in Einstein-Maxwell fields is related to super-energy tensors, providing quantities conserved along null hypersurfaces. Finally, conserved super-energy currents are found for any minimally coupled scalar field whenever there is a Killing vector.

8 pages, LaTeX, no figures. This essay received an Honorable Mention in the 1999 Essay Competition of the Gravity Research Foundation

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