No-Go Theorem for Energy-Momentum Conservation in Curved Spacetime
Abstract
It is pointed out that in curved spacetime, one cannot define the sum of energy-momemtum 4-vector over a space-like hypersurface. The difficulty in finding satisfactory gravitational energy-momentum complex stems from misunderstanding of this question. The law of conservation of energy-momentum holds valid only approximately when spacetime is not seriously curved.
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