Canonical superenergy tensors in general relativity

We present the concept of superenergy tensors in the framework of general relativity (GR). These tensors were introduced constructively by the author years ago and they were obtained by a suitable averaging of the energy-momentum tensors or pseudotensors. Because in GR the Einstein canonical energy-momentum pseudotensor (E)t(i)(k) of the gravitational field and the canonical energy-momentum complex K-E(i)k = root\g\(T-i(k) + (E)t(i)(k)), matter and gravitation, are physically distinguished, we confine this paper to the canonical superenergy tensor S-g(i)k Of the gravitational field Gamma(kl)(i) and to the canonical total superenergy tensor S-i(k) = S-g(i)k + S-m(i)k of matter and gravitation only. These superenergy tensors can be obtained by the above-mentioned averaging of the pseudotensor (E)t(i)(k) and complex K-E(i)k. We give the analytic forms of these two canonical superenergy tensors and show some of their possible applications in GR. The canonical superenergy tensor S-g(i)k of the gravitational field Gamma(kl)(i) can be used as a substitute for the nonexisting energy-momentum tensor of this field.