On the structure of the new electromagnetic conservation laws

• Published in: Classical and quantum gravity 2004-02, Vol.21 (4), p.L21-L25
• Main Author: Edgar, S Brian
• Format: Article
• Language: English
• Subjects: Classical general relativity; Exact sciences and technology; Fundamental problems and general formalism; General relativity and gravitation; MATEMATIK; MATHEMATICS; Physics
• ISSN: 0264-9381; 1361-6382; 1361-6382
• DOI: 10.1088/0264-9381/21/4/L04

New electromagnetic conservation laws have recently been proposed: in the absence of electromagnetic currents, the trace of the Chevreton superenergy tensor, Hab is divergence free in four-dimensional (a) Einstein spacetimes for test fields, and (b) Einstein-Maxwell spacetimes. Subsequently it has been pointed out, in analogy with flat spaces, that for Ricci-flat spacetimes the trace of the Chevreton superenergy tensor Hab can be rearranged in the form of a generalized wave operator □L acting on the energy-momentum tensor Tab of the test fields, i.e., H ab = □Ltab/2. In this letter we show, for Einstein-Maxwell spacetimes in the full nonlinear theory, that, although, the trace of the Chevreton superenergy tensor Hab can again be rearranged in the form of a generalized wave operator □G acting on the electromagnetic energy-momentum tensor, in this case the result is also crucially dependent on Einstein's equations, hence we argue that the divergence-free property of the tensor Hab = □GT ab/2 has significant independent content beyond that of the divergence-free property of Tab.