Gravitational energy

Gravitational energy is the energy associated with the gravitational field.

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According to classical mechanics, between two or more masses (or other forms of energy-momentum) a gravitational potential energy exists. Conservation of energy requires that this gravitational potential field energy is always negative.^[1]

In general relativity gravitational energy is modeled via the Landau-Lifshitz pseudotensor^[2] which allows the energy-momentum conservation laws of classical mechanics to be retained. Addition of the matter stress-energy-momentum tensor to Landau-Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor which has a vanishing divergence. Some people object to this derivation on the grounds that pseudotensors are inappropriate in general relativity, but this treatment only required, in the conservation law, the use of the derivative of the combined pseudotensor which was, in this case, in fact a tensor!

References

1. ^ Alan Guth The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (1997), Random House , ISBN 0-224-04448-6 Appendix A: Gravitational Energy demonstrates the negativity of gravitational energy.
2. ^ Lev Davidovich Landau & Evgeny Mikhailovich Lifshitz, The Classical Theory of Fields, (1951), Pergamon Press, ISBN 7-5062-4256-7