A new gravitational energy tensor

The Bel-Robinson tensor is the most used gravitational energy tensor; however, it has the dimensions of energy squared. How to construct tensors with the dimensions of energy by using Lancoz tensors is shown here. The resulting tensors have a large number of arbitrary parameters, frequently have spacelike currents, and frequently do not reduce to familiar pseudo-energy tensors in the weak field limit. Two particular examples of interest are one with well-behaved currents and one which reduces to an energy pseudo-tensor in the weak field limit.