Related papers: The Einstein-Vlasov System/Kinetic Theory
A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a…
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…
We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard-Balescu equations from the Klimontovich formalism. These equations take into account…
In this short note we present the dynamics of a general scalar-tensor model, and in particular a scalar Einstein-Gauss-Bonnet model with a non-minimal coupling between gravity and the kinetic term of the scalar field. For the sake of…
The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
Here we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed.…
We demonstrate that Einstein's general relativity theory arises as a special case in the framework of the Poincar\'e gauge theory of gravity under the assumption of a suitable nonminimal coupling of matter to the Riemann-Cartan geometry of…
We present a derivation of the mechanics of isothermal gas spheres directly from the Vlasov--Poisson equation. By extremising the Boltzmann entropy, we obtain the Maxwell--Boltzmann distribution for a self-gravitating isothermal Newtonian…
We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an…
Einstein-aether theory is general relativity coupled to a dynamical unit timelike vector field. A brief review of current theoretical understanding and observational constraints on the four coupling parameters of the theory is given.
We prove that Einstein's equations coupled to equations of Israel-Stewart-type, describing the dynamics of a relativistic fluid with bulk viscosity and nonzero baryon charge (without shear viscosity or baryon diffusion) dynamically coupled…
The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of…
Einstein utilized Lorentz invariance from Maxwell's equations to modify mechanical laws and establish the special theory of relativity. Similarly, we may have a different theory if there exists another covariance of Maxwell's equations. In…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…