Related papers: The Einstein-Vlasov system/Kinetic theory
We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in…
Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems.…
The method of obtaining of Vlasov-type equations for systems of interacting massive charged particles from the general relativistic Einstein-Hilbert action is considered. An effective approach to synchronizing the proper times of various…
The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys…
In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a collisionless…
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…
A kinetic model for the dynamics of collisionless spin neutral particles in a spacetime with torsion is proposed. The fundamental matter field is the kinetic density $f(x,u,s)$ of particles with four-velocity $u$ and four-spin $s$. The…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…
The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued…
In the general relativity theory the basic ingredient to describe gravity is the geometry, which interacts with all forms of matter and energy, and as such, the metric could be interpreted as a true physical quantity. However the metric is…
We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In…
Recent developments in observational cosmology have led to attempts to make modifications on both sides of the Einstein equation to explain some of the puzzling new findings. What follows is an examination of the source of gravity that we…
Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with positive curvature. In the case of the Universe consisting of massless particles the equation for R(t) is solved analytically.
Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim…
The kinetic approach to the formation of the filaments in the large-scale matter distribution in the Universe is considered within the Vlasov formalism. The structures arise due to the self-consistent dynamics, along with the repulsive term…
The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincar\'e…
Our current understanding of the Universe depends on the interplay of several distinct "matter" components, which interact mainly through gravity, and electromagnetic radiation. The nature of the different components, and possible…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable $z$ (radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced…