Related papers: The Boltzmann equation in special and general rela…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is…
We provide an exact analytical solution to the nonlinear relativistic Boltzmann equation for a homogeneous, anisotropically scattering massless gas. Utilizing a BKW-like trial solution, we cast the Boltzmann equation into a set of nonlinear…
In this paper, we consider the Boltzmann equation for a polyatomic gas. We establish that the mild solution to the Boltzmann equation on the torus is globally well-posed, provided the initial data that satisfy bounded velocity-weighted…
Using the accepted methods to extract natural system behavior from the Einstein-Hilbert gravitational field tensor equation, a new coordinate transformation is analyzed. It is demonstrated that these extraction methods yield specific…
In this paper, we first generalize the formulation of entropic gravity to (n+1)-dimensional spacetime. Then, we propose an entropic origin for Gauss-Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field…
We present an interesting connection between Einstein-Friedmann equations for the models of universe filled with scalar field and the special form of Abel equation of the first kind. This connection works in both ways: first, we show how,…
We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. The extension links seamlessly to the action integral for the gravitational field. The demand…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and…
Following an approach proposed by Rosser for deriving the transformation equations of volume charge density and current density we derive the transformation equations for the space-time coordinates of the same event, for the mass and the…
We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of…
In this article we consider the linear inelastic Boltzmann equation in presence of a uniform and fixed gravity field, in the case of Maxwell molecules. We first obtain a well-posedness result in the space of finite, non-negative Radon…
In this paper two things are done. First it is shown how a four dimensional gauged Wess-Zumino-Witten term arises from the five dimensional Einstein-Hilbert plus Gauss-Bonnet lagrangian with a special choice of the coefficients. Second, the…
Generalizing the collision term in the relativistic Boltzmann equation to include nonlocal effects, and using Grad's 14-moment approximation for the single-particle distribution function, we derive evolution equations for the relativistic…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…