Abstract
From a geometric perspective, we proved the following conclusions, that are against mainstream scholars’ viewpoint. (i) Vanishing of the covariant divergence of matter energy momentum flux density in entire spacetime is a conservation law of matter energy-momentum. It reads the net increase of matter energy-momentum in any infinitesimal neighborhood of spacetime is zero. Hence, introducing gravitational energy-momentum does not save, but destroys the law of energy-momentum conservation. (ii) Interaction or force in physics always means exchange of energy-momentum. The spacetime metric field (gravitational field in general relativity) does not exchange energy-momentum with all mass points and matter fields. Therefore, the metric field of spacetime does not carry energy-momentum, it's not a force field, and gravity is not a natural force. The spacetime metric field is the geometrical aspect of moving matter 4-dimensional continuum. It is not a matter field itself.

Keywords
gravitational energy-momentum, energy-momentum conservation in general relativity

Cite this paper
Zhaoyan Wu, Gravitational Waves Do Not Carry Energy-Momentum , SCIREA Journal of Physics. Volume 5, Issue 1, February 2020 | PP. 1-28.

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