On the gravitational angular momentum of rotating sources

TL;DR

This paper explores the gravitational angular momentum in the teleparallel formulation of general relativity, showing how it can be calculated as a surface integral and discussing its physical interpretation related to frame dragging.

Contribution

It provides a practical method for calculating gravitational angular momentum as a surface integral and analyzes its dependence on the frame in the teleparallel gravity framework.

Findings

Angular momentum can be computed as a surface integral in practical scenarios.

Total angular momentum is finite under certain asymptotic conditions.

Gravitational angular momentum relates to inertial frame dragging.

Abstract

The gravitational energy-momentum and angular momentum satisfy the algebra of the Poincare group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy-momentum may be written as a surface integral in the three-dimensional spacelike hypersurface, whereas the definition for the angular momentum is given by a volume integral. It turns out that in practical calculations of the angular momentum of the gravitational field generated by localized sources like rotating neutron stars, the volume integral reduces to a surface integral, and the calculations can be easily carried out. Similar to previous investigations in the literature, we show that the total angular momentum is finite provided a certain asymptotic behaviour is verified. We discuss the dependence of the gravitational angular momentum on the frame, and argue that it is a measure of the dragging of inertial frames.