Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

Abstract

In the context of the Hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present 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. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes.

Kerr geometry in $$f(T)$$ f ( T ) gravity

“…Then we applied the ansatz (22), and obtained a differential equation for λ by demanding the vanishing of the Weitzenböck invariant (29). This differential equation was particularly simple because of a good choice of coordinates: we used the chart employed in the Newman-Janis algorithm for passing from a Schwarzschild solution to a Kerr solution [54].…”

“…We will employ null tetrads as a useful tool for straightforwardly getting the result. We remark that different aspects of rotating black holes have been discussed in the context of TEGR [23][24][25][26][27]. Among the papers about Kerr spacetime in modified gravity, we can mention those referred to f (R) gravity [28][29][30][31].…”

Angular Momentum of the BTZ Black Hole in the Teleparallel Geometry

“…They are given by Eqs. (19) and (20), which represent relations between e ak and the momenta Π ak . Thus we define (primary constraints)…”

“…Moreover we know that the energy density of the gravitational field diverges in the limit r → ∞. 19) The gravitational angular momentum given by Eq. (44) has an opposite sign to the angular momentum J of the source.…”

Energy contents of some rotating spacetimes in teleparallel gravity

“…In this framework, Maluf et al (2002) defined gravitational energy, momentum and angular momentum using the literature (Maluf 1994). Adopting this procedure, many people (Maluf et al 2003;da Rocha-Neto and Castello-Branco 2003;Sharif andTaj 2010a, 2010b) computed energy and its contents for different solutions. Recently, we have also investigated energy and its relevant quantities for a class of regular black holes coupled with non-linear electrodynamics source (Sharif and Jawad 2010).…”