The Jacobi Curvature Operator in Semi Riemannian Geometry and the Energy Momentum Stress Tensor of the Gravitational Field

TL;DR

This paper proposes a generalization of the energy-momentum stress tensor in general relativity, identifying the Jacobi curvature tensor as representing the total energy-momentum, including gravitational effects.

Contribution

It introduces a novel interpretation of the Jacobi curvature tensor as the embodiment of total energy-momentum stress in general relativity.

Findings

Jacobi curvature tensor represents total energy-momentum including gravity

Justification for generalizing the energy-momentum tensor

Provides a new geometric perspective on gravitational energy

Abstract

We give a justification for generalizing the notion of the energy momentum stress tensor in general relativity which results in the Jacobi curvature tensor being the embodiment of total energy momentum stress including gravity in general relativity.