Witten's expression for gravitational energy

Abstract

The origin and physical interpretation of Witten's integral expression for gravitational energy is examined. It is shown that this expression (including nonzero ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$) arises naturally from a Hamiltonian treatment of classical supergravity, without consideration of the quantum theory. In addition, this expression is evaluated explicitly in several examples. It is found that the individual terms do not have a simple physical interpretation. New integral expressions are then introduced in which the gravitational energy divides naturally into a conformally invariant and nonconformally invariant contribution. It is argued that in certain circumstances these contributions can be interpreted as the gravitational radiation energy and total binding energy for strongly gravitating systems.