Gravitational energy

Gravitational energy is the energy associated with the gravitational field. This phrase is found frequently in scientific writings about quasars (quasi-stellar objects) and other active galaxies.

Newtonian mechanics

According to classical mechanics, between two or more masses (or other forms of 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.

The gravitational energy density is:

$u = \frac{ -|\mathbf{g}|^2}{8 \pi G} \, ,$

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

General relativity

Main article: 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 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.

See also

• Blazar
• Energy in the electric field
• Energy in the magnetic field
• Seyfert galaxy