Applications of Super-Energy Tensors

TL;DR

This paper reviews the applications of superenergy tensors in various physical and mathematical contexts, highlighting their role in conserved quantities, field propagation, and different gravitational theories.

Contribution

It provides a comprehensive summary of new results involving superenergy tensors and explores their diverse applications in physics and geometry.

Findings

Superenergy tensors help analyze causal propagation of fields.

Existence of infinite conserved quantities in Ricci-flat spacetimes.

Applications across different gravitational theories like General Relativity and supergravity.

Abstract

In this contribution I intend to give a summary of the new relevant results obtained by using the general superenergy tensors. After a quick review of the definition and properties of these tensors, several of their mathematical and physical applications are presented. In particular, their interest and usefulness is mentioned or explicitly analyzed in 1) the study of causal propagation of general fields; 2) the existence of an infinite number of conserved quantities in Ricci-flat spacetimes; 3) the different gravitational theories, such as Einstein's General Relativity or, say, $n=11$ supergravity; 4) the appearance of some scalars possibly related to entropy or quality factors; 5) the possibility of superenergy exchange between different physical fields and the appearance of mixed conserved currents.