Conserved Matter Superenergy Currents for Hypersurface Orthogonal 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.

13 pages

References in corpus (2)

• Conserved superenergy currents
• New electromagnetic conservation laws

Cited by in corpus (6)

• Dynamical laws of superenergy in General Relativity
• The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces
• Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups
• On the conservation of Superenergy and its applications
• On the energy content of electromagnetic and gravitational plane waves through super-energy tensors
• f-symbols, Killing tensors and conserved Bel-type currents