Related papers: Thomas-Fermi Model for a Bulk Self-Gravitating Ste…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
We complete previous investigations on the thermodynamics of self-gravitating systems by studying the grand canonical, grand microcanonical and isobaric ensembles. We also discuss the stability of polytropic spheres in the light of a…
In order to model the Fermi bubbles we apply the theory of the superbubble (SB). A thermal model and a self-gravitating model are reviewed. We introduce a third model based on the momentum conservation of a thin layer which propagates in a…
Motivated by the models of geometry with discrete spaces as additional dimensions we investigate the stability of cosmological solutions in models with two metrics of the Friedmann-Lema\^itre-Robertson-Walker type. We propose an effective…
The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (thermalization) of a many-body system. We review two approaches to this problem, the ergodic theory and Langevin (stochastic) equation ones, which have been applied…
We prove a theorem, using the density functional approach and relying on a classical result by Lieb and Simon on Thomas-Fermi model, showing that in the thermodynamic limit bulk matter is at most semiclassical and coherence preserving. The…
We analyze the cosmological solutions of $f(T,B)$ gravity using dynamical system analysis where $T$ is the torsion scalar and $B$ be the boundary term scalar. In our work, we assume two specific cosmological models. For first model, we…
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical…
The Thomas-Fermi model at finite temperature is extended to describe a system of self-gravitating weakly interacting massive fermions in a general-relativistic framework. By cooling a nondegenerate gas of weakly interacting massive fermions…
We study the stabilities and classical solutions of Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. In fact, we extend the study the stabilities of Euler-Poisson equations with or without frictional…
A model of static boson-fermion star with spherical symmetry based on the scalar-tensor theory of gravity with massive dilaton field is investigated numerically. Since the radius of star is \textit{a priori} an unknown quantity, the…
We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…
We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
The calculations in Thomas-Fermi approximation show that in a gravitational field each cell of ultra dense matter inside celestial bodies obtains a very small positive electric charge. A celestial body is electrically neutral as a whole,…
We present results of numerical modeling made for the galactic stellar and stellar-gas disk embedded in the spherical halo and bulge. The stellar disk is simulated by N-body system, the equations of hydrodynamics are solved by TVD-method.…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating…