Energy conservation and equivalence principle in General Relativity

TL;DR

This paper formulates a covariant energy conservation law in General Relativity using the generalized Stokes theorem and Path Group, extending Einstein's equivalence principle to include energy-momentum conservation without explicit gravitational field terms.

Contribution

It introduces a covariant integral form of energy-momentum conservation in curved spacetime, generalizing Einstein's equivalence principle.

Findings

Derived a covariant conservation law for energy-momentum in GR

Extended Einstein's equivalence principle to include energy conservation

Connected integrals in curved spacetime with Path Group formalism

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.