Gravitational energy

# Gravitational energy

Discussion

Encyclopedia
Gravitational energy is the energy associated with the gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

. This phrase is found frequently in scientific writings about quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s (quasi-stellar objects) and other active galaxies.

## Newtonian mechanics

According to classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

, between two or more mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

es (or other forms of energy-momentum) a gravitational potential energy exists, from which the gravitational field energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...

can be calculated. Conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

requires that this gravitational field energy is always negative.

The gravitational energy density is:

where G is Newton's gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

, and g is the gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

vector.

## General relativity

In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

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
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

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
Divergence
In vector calculus, divergence is a vector operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around...

in all frames; the vanishing divergence ensures the conservation law. Some people object to this derivation on the grounds that pseudotensor
Pseudotensor
In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation preserving coordinate transformation , but gains an additional sign flip under an orientation reversing coordinate transformation In physics and mathematics, a pseudotensor is usually...

s are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is a tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

.