Conserved superenergy currents

Abstract

We exploit once again the analogy between the energy–momentum tensor and the so-called ‘superenergy’ tensors in order to build conserved currents in the presence of Killing vectors. First of all, we derive the divergence-free property of the gravitational superenergy currents under very general circumstances, even if the superenergy tensor is not divergence-free itself. The associated conserved quantities are explicitly computed for the Reissner–Nordström and Schwarzschild solutions. The remaining cases, when the above currents are not conserved, lead to the possibility of an interchange of some superenergy quantities between the gravitational and other physical fields in such a manner that the total, mixed, current may be conserved. Actually, this possibility has been recently proved to hold for the Einstein–Klein–Gordon system of field equations. By using an adequate family of known exact solutions, we present explicit and completely non-obvious examples of such mixed conserved currents.