An alternative non-negative gravitational energy tensor to the Bel-Robinson tensor

TL;DR

This paper discusses an alternative tensor to the Bel-Robinson tensor that also provides positive gravitational energy in small regions, offering a new approach to gravitational energy representation.

Contribution

It introduces and analyzes the tensor V as a new candidate for representing gravitational energy, comparable to the Bel-Robinson tensor.

Findings

V tensor offers the same positivity as B tensor.

Both tensors serve as basis for non-negative gravitational energy expressions.

V tensor provides an alternative formulation in gravitational energy studies.

Abstract

The Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$ gives a positive definite gravitational energy in the small sphere limit approximation. However, there is an alternative tensor $V_{\alpha\beta\mu\nu}$ which was proposed recently that offers the same positivity as $B_{\alpha\beta\mu\nu}$ does. These two tensors are a basis for expressions which have the desirable non-negative gravitational energy in the small sphere region limit.