TOPOLOGICAL BLACK HOLES AND MOMENTUM FOUR-VECTOR

Abstract

We consider the energy–momentum definition of the Møller in both general relativity and teleparallel gravity to evaluate the energy distribution (due to both matter and fields including gravitation) associated with the topological black holes with a conformally coupled scalar field. Our results show that the energy depends on the mass M and charge Q of the black holes and cosmological constant Λ. In some special limits, the expression of the energy reduces to the energy of the well-known spacetimes. The results also support the viewpoint of Lessner that the Møller energy–momentum formulation is a powerful concept of the energy–momentum. Furthermore, the energy obtained in teleparallel gravity is also independent of the teleparallel dimensionless coupling constants which means that it is valid not only in the teleparallel equivalent of the general relativity but also in any teleparallel model.