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Paper IPM / Astronomy / 14100  


Abstract:  
tarting 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 MassTemperature 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 nonstatic 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
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