Covariant localization of gravitational energy in general relativity

Establish a coordinate-independent, covariant, tensorial formulation that localizes gravitational energy within general relativity by replacing non-covariant pseudotensor prescriptions with a true tensor that remains well-defined under general coordinate transformations.

Background

The paper reviews longstanding difficulties in defining energy in the gravitational field within classical general relativity. Einstein introduced a non-covariant pseudotensor to describe gravitational energy-momentum, but such pseudotensors depend on the coordinate system and therefore lack a generally accepted physical meaning.

Numerous energy-momentum complexes and quasi-local proposals have been advanced, yet their coordinate dependence or non-tensorial nature undermines universal acceptance. This motivates the explicit statement that the energy localization problem in GR remains unresolved, framing a central open issue that the paper seeks to address via a quantum-theoretic approach.