Energy and angular momentum densities of stationary gravitational fields

Abstract

We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary spacetimes. These expressions involve nonlocally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.