Dust solution

In general relativity, a dust solution is an 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 which has positive mass density but vanishing pressure. Dust solutions are by far the most important special case of fluid solutions in general relativity.

The pressureless perfect fluid in a dust solution can be interpreted as a model of a configuration of dust particles which interact with each other only gravitationally. 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 solutions 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 modeling rotating accretion disks are yet known due to the extreme mathematical difficulty of constructing them.