On the energy content of electromagnetic and gravitational plane waves through super-energy tensors

TL;DR

This paper investigates the energy content of electromagnetic and gravitational plane waves using super-energy tensors, analyzing single and colliding waves, and exploring the causality of super-momentum vectors in different regions.

Contribution

It provides a detailed analysis of energy content via super-energy tensors in both single and colliding wave scenarios, highlighting nonlinear effects in Einstein's theory.

Findings

Super-energy tensors effectively describe wave energy content.

Causality properties of super-momentum vectors vary between regions.

Nonlinear interactions significantly influence energy transfer in colliding waves.

Abstract

The energy content of (exact) electromagnetic and gravitational plane waves is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the --less familiar-- Chevreton tensors) and natural observers. Starting from the case of single waves, the more interesting situation of colliding waves is then discussed, where the nonlinearities of the Einstein's theory play an important role. The causality properties of the super-momentum four vectors associated with each of these tensors are also investigated when passing from the single-wave regions to the interaction region.