Gravitational energy, momentum and angular momentum of Schwarzschild Anti-de Sitter space-times in the teleparallel equivalent of general relativity

Abstract

We give a class of spherically symmetric-Anti de Sitter (Ads), exact solution in the teleparallel equivalent of general relativity (TEGR). The solution depends on an arbitrary function \(\mathcal{F}(R)\) and reproduce the metric of Schwarzschild Ads space-time. In the context of the Hamiltonian formulation of the TEGR we compute the gravitational energy of this class. The calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. We show that the form of the energy depends on the arbitrary function. We make a constrain on this arbitrary function to give the correct form of energy.