Bergmann-Thomson energy-momentum complex for solutions more general than the Kerr-Schild class

In a very well-known paper, Virbhadra's research group proved that the Weinberg, Papapetrou, Landau and Lifshitz, 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.