Physical decomposition of the gauge and gravitational fields

Physical decomposition of the non-Abelian gauge field has recently helped to achieve a meaningful gluon spin. Here we extend this approach to gravity and attempt a meaningful gravitational energy. The metric is unambiguously separated into a pure geometric term which contributes a null curvature tensor, and a physical term which represents the true gravitational effect and always vanishes in a flat space-time. By this decomposition the conventional pseudotensors of the gravitational stress-energy are easily rescued to produce a definite physical result. Our decomposition applies to any symmetric tensor, and has an interesting relation to the transverse-traceless decomposition discussed by Arnowitt, Deser and Misner, and by York.