On the gravitational angular momentum of rotating sources

Understand

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.