(SUPER)n-ENERGY FOR ARBITRARY FIELDS AND ITS INTERCHANGE: CONSERVED QUANTITIES

Abstract

Inspired by classical work of Bel and Robinson, a natural purely algebraic construction of super-energy (s-e) 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 s-e 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 s-e between different fields is shown. The discontinuity propagation law in Einstein–Maxwell fields is related to s-e tensors, providing quantities conserved along null hypersurfaces. Finally, conserved s-e currents are found for any minimally coupled scalar field whenever there is a Killing vector.