General Relativity
In general relativity gravitational energy is extremely complex, and there is no single agreed upon definition of the concept. It is sometimes modeled via the Landau-Lifshitz pseudotensor which allows the energy-momentum conservation laws of classical mechanics to be retained. Addition of the matter stress-energy-momentum tensor to the Landau-Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor which has a vanishing 4-divergence in all frames; the vanishing divergence ensures the conservation law. Some people object to this derivation on the grounds that pseudotensors are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is a tensor.
Read more about this topic: Gravitational Energy
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