Analysis of Jeans instability from the Boltzmann equation

The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. Two cases are analyzed: a system with baryonic and dark matter in a static universe and a single system in an expanding universe. The amplitudes of the perturbed distribution functions are considered as a linear combination of the collision invariants of the Boltzmann equation. For the system of baryonic and dark matter, the Jeans mass of the combined system is smaller than the one of the single system indicating that a smaller mass is needed to initiate the collapse. For the single system in an expanding universe it is not necessary to make use of Jeans "swindle"and it shown that for small wavelengths the density contrast oscillates while for large wavelengths it grows with time and the Jeans instability emerges.Comment: 10 pages, 1 figure, new analysi

Brane cosmology with a van der Waals equation of state

The evolution of a Universe confined onto a 3-brane embedded in a five-dimensional space-time is investigated where the cosmological fluid on the brane is modeled by the van der Waals equation of state. It is shown that the Universe on the brane evolves in such a manner that three distinct periods concerning its acceleration field are attained: (a) an initial accelerated epoch where the van der Waals fluid behaves like a scalar field with a negative pressure; (b) a past decelerated period which has two contributions, one of them is related to the van der Waals fluid which behaves like a matter field with a positive pressure, whereas the other contribution comes from a term of the Friedmann equation on the brane which is inversely proportional to the scale factor to the fourth power and can be interpreted as a radiation field, and (c) a present accelerated phase due to a cosmological constant on the brane.Comment: 9 pages, 2 figures, to be published in General Relativity and Gravitatio

The Boltzmann equation in special and general relativity

Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation. The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation proposed by Anderson and Witting. Two applications in general relativity are considered: one refers to a gas in a homogeneous and isotropic Universe where irreversible processes are present during its evolution; in the other it is analyzed a gas under the influence of a spherically symmetrical non-rotating and uncharged source of the gravitational field.Comment: 8 pages, contributed paper at the 28th International Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012) correction: eqs. (40), (42) and (43

Relative Entropy of a Freely Cooling Granular Gas

The time evolution and stationary values of the entropy per particle of a homogeneous freely cooling granular gas, relative to the maximum entropy consistent with the instantaneous translational and rotational temperatures, is analyzed by means of a Sonine approximation involving fourth-degree cumulants. The results show a rich variety of dependencies of the relative entropy on time and on the coefficients of normal and tangential restitution, including a peculiar behavior in the quasi-smooth limit.Comment: 6 pages; 2 figures; contributed paper at the 28th International Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012