Dust solution

In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure. Dust solutions are an important special case of fluid solutions in general relativity.

Dust model[edit]

A perfect and pressureless fluid can be interpreted as a model of a configuration of dust particles that locally move in concert and interact with each other only gravitationally, from which the name is derived. For this reason, dust models are often employed in cosmology as models of a toy universe, in which the dust particles are considered as highly idealized models of galaxies, clusters, or superclusters. In astrophysics, dust models have been employed as models of gravitational collapse. Dust solutions can also be used to model finite rotating disks of dust grains; some examples are listed below. If superimposed somehow on a stellar model comprising a ball of fluid surrounded by vacuum, a dust solution could be used to model an accretion disk around a massive object; however, no such exact solutions that model rotating accretion disks are yet known due to the extreme mathematical difficulty of constructing them.

(LTB) dusts (some of the simplest inhomogeneous cosmological models, often employed as models of gravitational collapse)

Lemaître–Tolman–Bondi

(cosmological models which exhibit perturbations from FLRW models)

Kantowski–Sachs dusts

Gödel metric

Lorentz group

Schutz, Bernard F. (2009), "4. Perfect fluids in special relativity", (2 ed.), Cambridge University Press, ISBN 978-0-521-88705-2

A first course in general relativity

Stephani, H.; Kramer, D.; MacCallum, M.; Hoenselaers, C.; Herlt, E. (2003). Exact Solutions of Einstein's Field Equations (2nd edn.). Cambridge: Cambridge University Press. 0-521-46136-7. Gives many examples of exact dust solutions.