Thermodynamics and Self-Gravitating Systems

Abstract

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 after sufficient time has gone by. Time dependent phenomena are beyond the scope of this paper. While thermodynamics is firmly rooted in statistical physics, equilibrium configurations, stability criteria and the destabilizing effect of fluctuations are all expressed in terms of thermodynamic functions. The work is not a review paper but a pedagogical introduction which may interest theoreticians in astronomy and astrophysicists. It contains sufficient mathematical details for the reader to redo all calculations. References are only to seminal works or readable reviews. (Except in the ultimate sub-section.) Delicate mathematical problems are mentioned but are not discussed in detail.

35 pages,6 figures

Cited by in corpus (50)

• Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: I. Analytical results
• Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: II. Numerical results
• The Phase Transition between Caged Black Holes and Black Strings - A Review
• Dynamics and thermodynamics of a simple model similar to self-gravitating systems: the HMF model
• Phase transitions between dilute and dense axion stars
• On the lifetime of metastable states in self-gravitating systems
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• Kinetic theory of spatially inhomogeneous stellar systems without collective effects
• Models of dark matter halos based on statistical mechanics: II. The fermionic King model
• Models of dark matter halos based on statistical mechanics: I. The classical King model
• Thermodynamical instabilities of perfect fluid spheres in General Relativity
• Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions
• Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes
• On the formation and stability of fermionic dark matter halos in a cosmological framework
• Self-gravitating Brownian systems and bacterial populations with two or more types of particles
• Isotropic-Nematic Phase Transitions in Gravitational Systems
• Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
• Critical dynamics of self-gravitating Langevin particles and bacterial populations
• Out-of-equilibrium phase transitions in the HMF model: a closer look
• Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|\phi {|}^4$ self-interaction
• Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential
• Caloric curves of self-gravitating fermions in general relativity
• Core mass -- halo mass relation of bosonic and fermionic dark matter halos harbouring a supermassive black hole
• Entropy of gravitating systems: scaling laws versus radial profiles
• Kinetic theory of collisionless relaxation for systems with long-range interactions
• Gravitational phase transitions and instabilities of self-gravitating fermions in general relativity
• Gravothermal Catastrophe: the dynamical stability of a fluid model
• A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
• Caloric curves of classical self-gravitating systems in general relativity
• Theory of Stellar Population Synthesis with an application to N-Body simulations
• Gravothermal Catastrophe with a Cosmological Constant
• Galaxy clusters and structure formation in quintessence versus phantom dark energy universe
• Thermodynamics of the HMF model with a magnetic field
• Gravitational phase transitions with an exclusion constraint in position space
• Relativistic Gravitational Phase Transitions and Instabilities of the Fermi Gas
• Gravitational instabilities of isothermal spheres in the presence of a cosmological constant
• Stars in M theory (made up of intersecting branes)
• Gravothermal instability with a cosmological constant in the canonical ensemble
• Equilibrium and Dynamical Evolution of Self-Gravitating System Embedded in a Potential Well
• Thermodynamic instabilities in holographic neutron stars at finite temperature
• Collisions of rigidly rotating disks of dust in General Relativity
• Holographic pressure and volume for black holes
• Scalar correlators and normal modes in holographic neutron stars
• Gravitational-thermodynamic instabilities of isothermal spheres in dS and AdS
• Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation
• A condensed-matter analogue of the false vacuum
• Thermodynamics and phase transitions of black holes in contact with a gravitating heat bath
• Derivation of an equation of pair correlation function from BBGKY hierarchy in a weakly coupled self gravitating system
• Self-gravitating isothermal sphere in an expanding background
• Thermodynamics of spherically symmetric thin-shell spacetimes