Energy-momentum of the gravitational field in the teleparallel geometry

TL;DR

This paper develops a Hamiltonian framework for the teleparallel equivalent of general relativity, providing definitions for gravitational energy, momentum, and angular momentum, and applies these to black hole physics.

Contribution

It introduces a Hamiltonian constraint-based approach to define gravitational energy-momentum and angular momentum in teleparallel gravity without gauge fixing.

Findings

Energy-momentum density derived from total divergence in constraints

Successful calculation of Kerr black hole's irreducible mass

Angular momentum defined via primary constraints satisfying algebra

Abstract

The Hamiltonian formulation of the teleparallel equivalent of general relativity without gauge fixing has recently been established in terms of the Hamiltonian constraint and a set of six primary constraints. Altogether, they constitute a set of first class constraints. In view of the constraint structure we establish definitions for the energy, momentum and angular momentum of the gravitational field. In agreement with previous investigations, the gravitational energy-momentum density follows from a total divergence that arises in the constraints. This definition is applied successfully to the calculation of the irreducible mass of the Kerr black hole. The definition of the algular momentum of the gravitational field follows from the integral form of primary constraints that satisfy the angular momentum algebra.