Related papers: Solvable model of a self-gravitating system
We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
The kinetic theory of a self-gravitating system is considered in the framework of Bhatnager-Gross-Krook model. This approach offers a unique and tractable setup for studying the central, collision-dominated region of the system, as well as…
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…
After introducing the fundamental properties of self-gravitating systems, we present an application of Tsallis' generalized entropy to the analysis of their thermodynamic nature. By extremizing the Tsallis entropy, we obtain an equation of…
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 introduce a simple model of hard spheres with gravitational interactions, for which we study a suitable scaling limit. Usual extensive properties are maintained notwithstanding the long range of gravitational interaction. We show that a…
Self-gravitating systems, like globular clusters or elliptical galaxies, are the prototypes of many-body systems with long-range interactions, and should be the natural arena where to test theoretical predictions on the statistical…
The thermodynamics of a self-gravitating gas cloud of particles interacting only via their gravitational potential is an interesting problem with peculiarities arising due to the long-ranged nature of the gravitational interaction. Based on…
We consider a general non-linear sigma model coupled to Einstein gravity and show that in spherical symmetry and for a simple realization of self-similarity, the spacetime can be completely determined. We also examine some more specific…
Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a…
We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both…
Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small "test" objects. In this note, I will consider models of finite…
We consider a Gaudin magnet (central spin model) with a time-dependent exchange couplings. We explicitly show that the Schr\"odinger equation is analytically solvable in terms of generalized hypergeometric functions for particular choices…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
A system of self-gravitating massive fermions is studied in the framework of the general-relativistic Thomas-Fermi model. We study the properties of the free energy functional and its relation to Einstein's field equations. A…
Equilibrium configurations for a self-gravitating scalar field with self-interaction are constructed. The corresponding Schr\"odinger-Poisson (SP) system is solved using finite differences assuming spherical symmetry. It is shown that…
The self-consistent Gaussian approximation (SCGA) for classical spin systems described by a completely anisotropic D-component vector model is proposed, which takes into account fluctuations of the molecular field and thus is a next step…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…