Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry

TL;DR

This paper calculates the gravitational energy of Kerr and Kerr-AdS black holes using teleparallel gravity, providing exact results for finite regions and at the event horizon, advancing understanding of gravitational energy in these spacetimes.

Contribution

It introduces a method to compute gravitational energy in Kerr and Kerr-AdS spacetimes within teleparallel gravity, applicable to finite regions and horizons.

Findings

Exact energy calculations for Kerr and Kerr-AdS spacetimes.

Energy evaluated at arbitrary finite regions and horizons.

No restrictions on black hole parameters.

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.