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.