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'''Gravitational energy''' is [[potential energy]] associated with the [[gravitational field]].  This phrase is found frequently in scientific writings about [[quasar]]s (quasi-stellar objects) and other [[active galaxies]].  Quasars generate and emit their energy from a very small region.  The emission of large amounts of power from a small region requires a power source far more efficient than the nuclear fusion that powers stars. The release of gravitational energy<ref name="Lambourne">{{Cite book |title=Relativity, Gravitation and Cosmology |author=Lambourne, Robert J. A. |url=http://books.google.com/books?id=GUySYQaDM1cC&pg=PA222&dq=the+release+of+gravitational+energy+by+matter&hl=en&sa=X&ei=JvirUKTBMobo8gTrxYHgDQ&ved=0CC0Q6AEwAA#v=onepage&q=the%20release%20of%20gravitational%20energy%20by%20matter&f=false |edition=Illustrated |year=2010 |publisher=Cambridge University Press |isbn=0521131383 |page=222 |accessdate=2012-11-20}}</ref> by matter falling towards a massive black hole is the only process known that can produce such high power continuously. Stellar explosions – [[supernova]]s and [[gamma-ray burst]]s – can do so, but only for a few weeks.<ref name="Lambourne" />

== Newtonian mechanics ==

According to [[classical mechanics]], between two or more [[mass]]es (or other forms of [[energy-momentum 4-vector|energy-momentum]]) a gravitational potential energy exists, from which the gravitational field [[energy density]] can be calculated. [[Conservation of energy]] requires that this gravitational field energy is always negative.<ref>[[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.</ref>  

The gravitational energy density is:
:<math> u = \frac{ -|\mathbf{g}|^2}{8 \pi G} \, ,</math><ref>[http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/possible_scalar_terms.htm NASA site] Gravitational energy density by analogy with EM</ref>

where ''G'' is Newton's [[gravitational constant]], and '''g''' is the [[gravitational field]] vector.

== General relativity ==

{{Main|Mass in 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]]<ref>[[Lev Davidovich Landau]] & [[Evgeny Mikhailovich Lifshitz]], ''The Classical Theory of Fields'', (1951), Pergamon Press, ISBN 7-5062-4256-7</ref> 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 [[pseudotensor]]s are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is a [[tensor]].

== See also ==

* [[Gravitational binding energy]]
* [[Gravitational potential]]
* [[Standard gravitational parameter]]
* [[Gravitational wave]]

== References ==

{{Reflist}} 

<!--Categories-->
[[Category:Forms of energy]]
[[Category:Gravitation]]
[[Category:Conservation laws]]
[[Category:Tensors in general relativity]]


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