Bergmann–Thomson Energy-Momentum Complex for Solutions More General than the Kerr–Schild Class

Abstract In a very well-known paper, Virbhadra’s research group proved that the Weinberg, Papapetrou, Landau and Lifhsitz, and Einstein energy-momentum complexes “coincide” for all metrics of Kerr–Schild class. A few years later, Virbhadra clarified that this “coincidence” in fact holds for metrics more general than the Kerr–Schild class. In the present paper, this study is extended for the Bergmann–Thomson complex and it is proved that this complex also “coincides” with those complexes for a more general than the Kerr–Schild class metric.