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The Einstein pseudo-tensor and the flux integral for perturbed static space-times. (English) Zbl 0744.53038
Authors’ summary: “The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorithm. A similar earlier effort with the aid of the Landau-Lifschitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing features that its second variation retains its divergence- free property provided only the equations governing the static space-time and its linear perturbations are satisfied.
When one seeks the corresponding flux integral for Einstein-Maxwell space-times, the common procedure of including, together with the pseudo- tensor, the energy-momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.”.

MSC:
53Z05 Applications of differential geometry to physics
83C40 Gravitational energy and conservation laws; groups of motions
53B50 Applications of local differential geometry to the sciences
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