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Collisionless self-gravitating statistical systems of scalarly interacting particles. (English) Zbl 1342.83535

Summary: We consider the theory of collisionless statistical systems with interparticle scalar interaction. A mathematical model of such systems is constructed, and an exact solution of the Vlasov equation for the isotropic homogenous model of the Universe is found. Asymptotic solutions of the self-consistent Vlasov-Einstein model for conformally invariant scalar interactions are found. We obtain and study an exact cosmological solution of a self-consistent set of equations consisting of a collisionless kinetic equation for a plasma with interparticle scalar interaction and the scalar field equation with a source. It is shown that in the ultrarelativistic limit the scalar interaction of particles leads to generation of an effective mass of scalar bosons.

MSC:

83F05 Relativistic cosmology
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C15 Exact solutions to problems in general relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
62P35 Applications of statistics to physics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
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References:

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