On the structure of the new electromagnetic conservation laws

TL;DR

This paper investigates new electromagnetic conservation laws related to the Chevreton superenergy tensor in Einstein-Maxwell spacetimes, showing that its divergence-free property has independent significance beyond the energy-momentum tensor.

Contribution

It demonstrates that in Einstein-Maxwell spacetimes, the divergence-free property of the Chevreton superenergy tensor is fundamentally linked to Einstein's equations, extending previous flat space results.

Findings

The trace of the Chevreton tensor can be expressed as a wave operator acting on the energy-momentum tensor.

The divergence-free property of the Chevreton tensor depends on Einstein's equations in non-linear theory.

This property has independent physical significance beyond the energy-momentum tensor.

Abstract

New electromagnetic conservation laws have recently been proposed: in the absence of electromagnetic currents, the trace of the Chevreton superenergy tensor, $H_{ab}$ is divergence-free in four-dimensional (a) Einstein spacetimes for test fields, (b) Einstein-Maxwell spacetimes. Subsequently it has been pointed out, in analogy with flat spaces, that for Einstein spacetimes the trace of the Chevreton superenergy tensor $H_{ab}$ can be rearranged in the form of a generalised wave operator $\square_L$ acting on the energy momentum tensor $T_{ab}$ of the test fields, i.e., $H_{ab}=\square_LT_{ab}/2$. In this letter we show, for Einstein-Maxwell spacetimes in the full non-linear theory, that, although, the trace of the Chevreton superenergy tensor $H_{ab}$ can again be rearranged in the form of a generalised wave operator $\square_G$ 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 $H_{ab}=\square_GT_{ab}/2$ has significant independent content beyond that of the divergence-free property of $T_{ab}$.