Relativistic Gravitational Phase Transitions and Instabilities of the Fermi Gas

Abstract

We describe microcanonical phase transitions and instabilities of the ideal Fermi gas in general relativity at nonzero temperature confined in the interior of a spherical shell. The thermodynamic behaviour is governed by the compactness of rest mass, namely of the total rest mass over radius of the system. For a fixed value of rest mass compactness, we study the caloric curves as a function of the size of the spherical box. At low compactness values, low energies and for sufficiently big systems the system is subject to a gravothermal catastrophe, which cannot be halted by quantum degeneracy pressure, and the system collapses towards the formation of a black hole. For small systems, there appears no instability at low energies. For intermediate sizes, between two marginal values, gravothermal catastrophe is halted and a microcanonical phase transition occurs from a gaseous phase to a condensed phase with a nearly degenerate core. The system is subject to a relativistic instability at low energy, when the core gets sufficiently condensed above the Oppenheimer-Volkoff limit. For sufficiently high values of rest mass compactness the microcanonical phase transitions are suppressed. They are replaced either by an Antonov type gravothermal catastrophe for sufficiently big systems or by stable equilibria for small systems. At high energies the system is subject to the `relativistic gravothermal instability', identified by Roupas in [1], for all values of compactness and any size.

References in corpus (15)

• Composition and Structure of Protoneutron Stars
• The Equation of State of Hot, Dense Matter and Neutron Stars
• Gravitational instability of finite isothermal spheres
• Gravitational instability of isothermal and polytropic spheres
• Statistical Mechanics of the Self-Gravitating Gas: I. Thermodynamic Limit and Phase Diagram
• Thermodynamics and Self-Gravitating Systems
• Gravitational Phase Transition of Heavy Neutrino Matter
• Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars
• Statistical Mechanics of the Self-Gravitating Gas: II. Local Physical Magnitudes and Fractal Structures
• Thermodynamical instabilities of perfect fluid spheres in General Relativity
• Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes
• Relativistic Gravothermal Instabilities
• Corrigendum to "Thermodynamical instabilities of perfect fluid spheres in General Relativity"
• Thermal Mass limit of Neutron Cores
• Gravitational instability caused by the weight of heat

Cited by in corpus (12)

• On the formation and stability of fermionic dark matter halos in a cosmological framework
• Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
• Dynamical Instability of Collapsed Dark Matter Halos
• Caloric curves of self-gravitating fermions in general relativity
• Predictive model of fermionic dark matter halos with a quantum core and an isothermal atmosphere
• Gravitational phase transitions and instabilities of self-gravitating fermions in general relativity
• Caloric curves of classical self-gravitating systems in general relativity
• Gravitational instability caused by the weight of heat
• The Gravothermal Instability at all scales: from Turnaround Radius to Supernovae
• Supernova implosion-explosion in the light of catastrophe theory
• On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-Dimensional Spacetime
• Non-local Interactions are Essential Elements for Dark Matter Halo Stability: A Cross-Model Study