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arXiv · 2608.18459

Covariant Energy Momentum Tensor in General Relativity by Generalized Canonical Method

Masakatsu Kenmoku
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Abstract

Defining a complete and covariant energy-momentum tensor in general relativity is a longstanding issue of concern. A widely attempted approach is to define it as a pseudo-tensor in an asymptotic Lorentz system. In this paper, we present a complete covariant definition of the gravitational energy-momentum tensor in the generalized canonical form. The key is incorporate higher-order differential terms of the metric tensor into the gravitational action in order to derive the energy-momentum tensor consistently. This completely covariant form ensures that the gravitational energy is correctly obtained in any coordinate system, including polar coordinates and asymptotic Lorentz systems.

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Masakatsu Kenmoku. 2026-08-19. Covariant Energy Momentum Tensor in General Relativity by Generalized Canonical Method. https://arxiv.org/abs/2608.18459

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