paper

Energy and angular momentum of charged rotating black holes

arXiv:gr-qc/9501002 · doi:10.1007/BF02109529

Abstract

We show that the pseudotensors of Einstein, Tolman, Landau and Lifshitz, Papapetrou, and Weinberg (ETLLPW) give the same distributions of energy, linear momentum and angular momentum, for any Kerr-Schild metric. This result generalizes a previous work by Gürses and Gürsey that dealt only with the pseudotensors of Einstein and Landau and Lifshitz. We compute these distributions for the Kerr-Newman and Bonnor-Vaidya metrics and find reasonable results. All calculations are performed without any approximation in Kerr-Schild Cartesian coordinates. For the Reissner-Nordström metric these definitions give the same result as the Penrose quasi-local mass. For the Kerr black hole the entire energy is confined to its interior whereas for the Kerr-Newman black hole, as expected, the energy is shared by its interior as well as exterior. The total energy and angular momentum of the Kerr-Newman black hole are and , respectively ( is the mass parameter and is the rotation parameter). The energy distribution for the Bonnor-Vaidya metric is the same as the Penrose quasi-local mass obtained by Tod.

18 pages, no figures, REVTeX. This is a revised version with the same results, but we now use a previous work by Gürses and Gürsey to put our results in perspective

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