Localization of Energy-Momentum for a Black Hole Spacetime Geometry with Constant Topological Euler Density

Abstract

The evaluation of the energy-momentum distribution for a new four-dimensional, spherically symmetric, static and charged black hole spacetime geometry with constant nonzero topological Euler density is performed by using the energy-momentum complexes of Einstein and Møller. This black hole solution was recently developed in the context of the coupled Einstein–nonlinear electrodynamics of the Born-Infeld type. The energy is found to depend on the mass M and the charge q of the black hole, the cosmological constant Λ, and the radial coordinate r, while in both prescriptions all the momenta vanish. Some limiting and particular cases are analyzed and discussed, illustrating the rather extraordinary character of the spacetime geometry considered.