Gravitational waves and energy momentum quanta

Abstract

We review the role of the classical stress-energy tensor in defining the concept of energy and its conservation in classical field theory. Conserved electromagnetic currents associated with spacetime Killing symmetries are discussed in an attempt to draw analogies with the concepts of photons and gravitons. By embedding Einstein's original formulation of General Relativity into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor T-G is constructed from a contraction of the Bel tenser with a symmetric covariant second degree tensor field Phi that has a form analogous to the stress-energy tensor of the Maxwell field in an arbitrary space-time. For plane-fronted gravitational waves helicity-2 polarised (graviton) states can be identified carrying non-zero energy and momentum.