Gravitational phase transitions and instabilities of self-gravitating fermions in general relativity

TL;DR

This paper explores gravitational phase transitions and instabilities in self-gravitating fermion gases within general relativity, highlighting quantum effects that prevent collapse below the Oppenheimer-Volkoff limit and describing different collapse scenarios in microcanonical and canonical ensembles.

Contribution

It provides a detailed analysis of gravitational phase transitions in fermionic systems, including the impact of quantum mechanics and ensemble differences on collapse behavior.

Findings

Quantum mechanics prevents complete collapse below the Oppenheimer-Volkoff limit.

Fermionic systems undergo a phase transition from gaseous to condensed states.

Different collapse mechanisms occur in microcanonical and canonical ensembles.

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 $E<E_c$ and low temperatures $T<T_c$. 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 ($N<N_{\rm OV}$), 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 $N>N_{\rm OV}$, there can be a subsequent gravitational collapse below a lower critical energy $E<E''_c$ or a lower critical temperature $T<T'_c$ 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).