The Einstein PseudoTensor and the Flux Integral for Perturbed Static SpaceTimes
Abstract
The flux integral for axisymmetric polar perturbations of static vacuum spacetimes, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudotensor by a simple algorism. A similar earlier effort with the aid of the LandauLifshitz pseudotensor failed. The success with the Einstein pseudotensor is due to its special distinguishing feature that its second variation retains its divergencefree property provided only the equations governing the static spacetime and its linear perturbations are satisfied. When one seeks the corresponding flux integral for EinsteinMaxwell spacetimes, the common procedure of including, together with the pseudotensor, the energymomentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined `Noether operator', succeeds.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 December 1991
 DOI:
 10.1098/rspa.1991.0167
 Bibcode:
 1991RSPSA.435..645C