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

TL;DR

This paper introduces a purely algebraic construction of super-energy tensors applicable to arbitrary fields, revealing conserved quantities and energy interchange properties, with implications for global analysis and Einstein-Maxwell theory.

Contribution

It presents a new algebraic framework for super-energy tensors that possess desirable mathematical and physical properties, including conserved quantities and energy interchange mechanisms.

Findings

Existence of super-energy tensors with the dominant property.

Infinite conserved quantities in Special Relativity.

Super-energy interchange between different fields.

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.