Conserved Matter Superenergy Currents for Hypersurface Orthogonal Killing Vectors

TL;DR

This paper demonstrates that in four-dimensional Einstein-Maxwell spacetimes with hypersurface orthogonal Killing vectors, certain superenergy currents are conserved and proportional to the Killing vectors, supporting the concept of conserved superenergy currents.

Contribution

It extends the understanding of conserved superenergy currents to include Chevreton and Bel tensors in specific Einstein-Maxwell spacetimes with hypersurface orthogonal Killing vectors.

Findings

Chevreton superenergy currents are conserved and proportional to Killing vectors.

Bel currents are conserved, supporting the concept of conserved superenergy currents.

Scalar field currents are also conserved and proportional to Killing vectors.

Abstract

We show that for hypersurface orthogonal Killing vectors, the corresponding Chevreton superenergy currents will be conserved and proportional to the Killing vectors. This holds for four-dimensional Einstein-Maxwell spacetimes with an electromagnetic field that is sourcefree and inherits the symmetry of the spacetime. A similar result also holds for the trace of the Chevreton tensor. The corresponding Bel currents have previously been proven to be conserved and our result can be seen as giving further support to the concept of conserved mixed superenergy currents. The analogous case for a scalar field has also previously been proven to give conserved currents and we show, for completeness, that these currents also are proportional to the Killing vectors.