Gravitational Energy-Momentum and Conservation of Energy-Momentum in General Relativity

• Published in: Communications in theoretical physics Vol. 65; no. 6; pp. 716 - 730
• Main Author: 吴兆颜
• Format: Journal Article
• Language: English
• Published: Chinese Physical Society and IOP Publishing 01.06.2016
• Subjects: Conservation; energy-momentum conservation; Exchange; Gravitation; gravitational energy-momentum; Gravitational fields; Mathematical analysis; non-localizability; pseudotensor; Relativity; Variational principles; Vectors (mathematics); 广义变分原理; 广义相对论; 引力场; 曲线坐标系; 物质能量; 能量动量守恒定律; 能量动量张量; 能量守恒定律
• ISSN: 0253-6102; 1572-9494
• DOI: 10.1088/0253-6102/65/6/716

Based on a general variational principle, Einstein–Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a result of mistaking different geometrical, physical ob jects as one and the same. It is also pointed out that in a curved spacetime, the sum vector of matter energy-momentum over a finite hyper-surface can not be defined. In curvilinear coordinate systems conservation of matter energy-momentum is not the continuity equations for its components. Conservation of matter energy-momentum is the vanishing of the covariant divergence of its density-flux tensor field. Introducing gravitational energy-momentum to save the law of conservation of energy-momentum is unnecessary and improper. After reasonably defining ＂change of a particle＇s energy-momentum＂, we show that gravitational field does not exchange energy-momentum with particles. And it does not exchange energy-momentum with matter fields either. Therefore, the gravitational field does not carry energy-momentum, it is not a force field and gravity is not a natural force.