Energy and angular momentum of the gravitational field in the teleparallel geometry

TL;DR

This paper explores the Hamiltonian formulation of teleparallel gravity, providing new definitions for gravitational energy and angular momentum, and applies these to Kerr black holes and rotating mass shells.

Contribution

It introduces integral-based definitions of gravitational energy and angular momentum within teleparallel gravity and applies them to specific astrophysical scenarios.

Findings

Energy within Kerr black hole horizon closely matches irreducible mass

Defined gravitational angular momentum for a rotating mass shell

Provided consistent energy-momentum expressions in teleparallel framework

Abstract

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell.