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Energy conservation and equivalence principle in General Relativity

Michael B. Mensky
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Abstract

The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the energy-momentum of matter is then derived in General Relativity. It extends Einstein's equivalence principle on the energy conservation, since it formulates the conservation law for the energy-momentum of matter without explicit including the gravitational field in the formulation.

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Michael B. Mensky. 2004-09-30. Energy conservation and equivalence principle in General Relativity. https://doi.org/10.1016/j.physleta.2004.06.040

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