Relativistic virial relation for cosmological structures

Abstract

Starting with the relativistic Boltzmann equation for a system of particles defined by a distribution function, we have derived the virial relation for a spherical structure within an expanding background in the context of general relativity. This generalized form of the virial relation is then applied to the static case of a spherically symmetric structure to see the difference in the simplest case to the Newtonian relation. A relativistic Mass-Temperature relation for this simple case is also derived which can be applied to compact objects in astrophysics. Our general virial relation is then applied to the non-static case of a structure within an expanding universe where an extra term, usually missed in studies of structures in the presence of the dark energy, appears.

8 pages

References in corpus (5)

• The virial theorem and the dynamics of clusters of galaxies in the brane world models
• Relativistic Effect in Galaxy Clustering
• Large-Scale Structure Observables in General Relativity
• Cosmological black holes: the spherical perfect fluid collapse with pressure in a FRW background
• The virial theorem in Eddington-Born-Infeld gravity

Cited by in corpus (5)

• Spherical collapse and virialization in $f(T)$ gravities
• The Effect of Interacting Dark Energy on Mass-Temperature Relation in Galaxy Clusters
• Point mass Cosmological Black Holes
• Long gradient mode and large-scale structure observables
• Nonlinear phenomena in general relativity