Abstract
We discuss the occurrence of gravitational phase transitions and instabilities in a gas of self-gravitating fermions within the framework of general relativity. In the classical (nondegenerate) limit, the system undergoes a gravitational collapse at low energies E<Ec and low temperatures T<Tc. This is called “gravothermal catastrophe” in the microcanonical ensemble and “isothermal collapse” in the canonical ensemble. When quantum mechanics is taken into account and when the particle number is below the Oppenheimer-Volkoff limit (N<NOV), complete gravitational collapse is prevented by the Pauli exclusion principle. In that case, the Fermi gas undergoes a gravitational phase transition from a gaseous phase to a condensed phase. The condensed phase represents a compact object like a white dwarf, a neutron star, or a dark matter fermion ball. When N>NOV, there can be a subsequent gravitational collapse below a lower critical energy E<Ec″ or a lower critical temperature T<Tc′ leading presumably to the formation of a black hole. The evolution of the system is different in the microcanonical and canonical ensembles. In the microcanonical ensemble, the system takes a “core-halo” structure. The core consists in a compact quantum object or a black hole while the hot halo is expelled at large distances. This is reminiscent of the red giant structure of low-mass stars or the implosion-explosion of massive stars (supernova). In the canonical ensemble, the system collapses as a whole towards a compact object or a black hole. This is reminiscent of the implosion of supermassive stars (hypernova).
Highlights
The study of phase transitions is an important problem in physics
The thermodynamics of the self-gravitating Fermi gas can have application in relation to the physics of white dwarfs, neutron stars and dark matter halos made of massive neutrinos
In this Letter, we report the results of our recent investigations concerning the statistical mechanics of selfgravitating fermions at finite temperature in the framework of general relativity
Summary
The study of phase transitions is an important problem in physics. Some examples include solid-liquid-gas phase transitions, superconducting and superfluid transitions, Bose-Einstein condensation, liquid-glass phase transition in polymers, liquid crystal phases, Kosterlitz-Thouless transition etc. The statistical mechanics of self-gravitating systems dates back to the works of Antonov [7] and LyndenBell and Wood [8] who considered nonrelativistic classical stellar systems such as globular clusters They enclosed the gas of stars within a spherical box of radius R in order to prevent its evaporation. The statistical mechanics of self-gravitating fermions at finite temperature in the nonrelativistic limit was developed by Hertel and Thirring [17], Bilic and Viollier [18] and Chavanis [3, 19] They showed that a gas of fermions experiences a gravitational phase transition from a gaseous phase to a condensed phase when the energy or the temperature passes below a critical value. In this Letter, we emphasize the main results of our study and refer to our companion papers for more details and additional results
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