Xiang-Song Chen and Ben-Chao Zhu
Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing 210093, China
Kavli Institute for Theoretical Physics China, CAS, Beijing 100190, China
(Received 15 October 2009; revised manuscript received 22 February 2011; published 6 April 2011)

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.