Black Hole Cold Brew: Fermi Degeneracy Pressure

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.