On a characteristic initial value problem in Plasma physics

The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions isolated from incoming radiation. Various consequences of the mass-energy conservation and of the absence of incoming radiation condition are first derived assuming the existence of global smooth solutions. In the spherically symmetric case, the existence of a unique classical solution in the future of the initial cone follows by arguments similar to the case of initial data at time $t=0$. The total mass-energy of spherically symmetric solutions equals the (properly defined) mass-energy on backward and forward light cones.Comment: 16 pages. Version in pres

Outgoing radiation from an isolated collisionless plasma

The asymptotic properties at future null infinity of the solutions of the relativistic Vlasov-Maxwell system whose global existence for small data has been established by the author in a previous work are investigated. These solutions describe a collisionless plasma isolated from incoming radiation. It is shown that a non-negative quantity associated to the plasma decreases as a consequence of the dissipation of energy in form of outgoing radiation. This quantity represents the analogue of the Bondi mass in general relativity.Comment: 13 pages; version in press. This paper continues the analysis started in math-ph/021101

Global classical solutions to the 3D Nordstr\"om-Vlasov system

The Nordstr\"om-Vlasov system describes the evolution of self-gravitating collisionless matter in the framework of a relativistic scalar theory of gravitation. We prove global existence and uniqueness of classical solutions for the corresponding initial value problem in three dimensions when the initial data for the scalar field are smooth and the initial particle density is smooth with compact support.Comment: 11 Pages, no figure

Cosmological models with fluid matter undergoing velocity diffusion

A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a cosmological scalar field term is added to the left hand side of the Einstein equations. This hypothesis promotes diffusion to a new mechanism for accelerated expansion in cosmology. It is shown that diffusion alters not only quantitatively, but also qualitatively the global dynamical properties of the standard cosmological models.Comment: 11 Pages, 4 Figures. Version in pres

Cosmology with matter diffusion

We construct a viable cosmological model based on velocity diffusion of matter particles. In order to ensure the conservation of the total energy-momentum tensor in the presence of diffusion, we include a cosmological scalar field $\phi$ which we identify with the dark energy component of the Universe. The model is characterized by only one new degree of freedom, the diffusion parameter $\sigma$. The standard $\Lambda$CDM model can be recovered by setting $\sigma=0$. If diffusion takes place ($\sigma >0$) the dynamics of the matter and of the dark energy fields are coupled. We argue that the existence of a diffusion mechanism in the Universe can serve as a theoretical motivation for interacting models. We constrain the background dynamics of the diffusion model with Supernovae, H(z) and BAO data. We also perform a perturbative analysis of this model in order to understand structure formation in the Universe. We calculate the impact of diffusion both on the CMB spectrum, with particular attention to the integrated Sachs-Wolfe signal, and on the matter power spectrum $P(k)$. The latter analysis places strong constraints on the magnitude of the diffusion mechanism but does not rule out the model.Comment: 20 pages, 8 figures, accepted for publication in JCA

The non-relativistic limit of the Nordstr\"om-Vlasov system

The Nordstr\"om-Vlasov system provides an interesting relativistic generalization of the Vlasov-Poisson system in the gravitational case, even though there is no direct physical application. The study of this model will probably lead to a better mathematical understanding of the class of non-linear systems consisting of hyperbolic and transport equations. In this paper it is shown that solutions of the Nordstr\"om-Vlasov system converge to solutions of the Vlasov-Poisson system in a pointwise sense as the speed of light tends to infinity, providing a further and rigorous justification of this model as a \textit{genuine} relativistic generalization of the Vlasov-Poisson system.Comment: 19 page