Gravitational Superenergy Tensor

TL;DR

This paper establishes a physical foundation for the local gravitational superenergy tensor and derives a gravitational stress-energy tensor analogous to electromagnetism, demonstrated through a plane gravitational wave example.

Contribution

It introduces a physical basis for the gravitational superenergy tensor and derives a local gravitational stress-energy tensor using gravitoelectromagnetic methods.

Findings

Derived a local gravitational superenergy tensor.

Identified a gravitational stress-energy tensor analogous to Maxwell's.

Illustrated the concepts with a plane gravitational wave.

Abstract

We provide a physical basis for the local gravitational superenergy tensor. Furthermore, our gravitoelectromagnetic deduction of the Bel-Debever-Robinson superenergy tensor permits the identification of the gravitational stress-energy tensor. This {\it local} gravitational analog of the Maxwell stress-energy tensor is illustrated for a plane gravitational wave.