Black Hole Cold Brew: Fermi Degeneracy Pressure

TL;DR

This paper explores how Fermi degeneracy pressure influences the stability of self-gravitating quantum systems, revealing conditions under which it can either prevent or promote collapse, with implications for early Universe black hole formation.

Contribution

It introduces a detailed analysis of quantum gravitational stability using Fermi-Dirac statistics and the TOV equation, highlighting the dual role of Fermi pressure in Newtonian and relativistic regimes.

Findings

Fermi pressure stabilizes systems against collapse in Newtonian gravity.

In general relativity, Fermi pressure can induce instability and collapse.

Critical mass at low temperatures is independent of boundary conditions.

Abstract

We investigate the dynamical instability of a self-gravitating thermal system in the quantum regime, where Fermi degeneracy pressure becomes significant. Using a truncated Fermi-Dirac distribution and solving the Tolman-Oppenheimer-Volkoff equation, we identify marginally stable configurations following Chandrasekhar's criterion. While Fermi pressure stabilizes a system against gravitational collapse in Newtonian gravity, in general relativity it can instead drive the instability, enabling collapse even at low temperatures. In the low-temperature limit, the critical mass is independent of the boundary temperature. We discuss implications for the formation of massive black holes in the early Universe through the gravothermal collapse of dark matter.