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

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.

7 pages