# Gravitational phase transition of self-gravitating systems of fermions in General Relativity

## TL;DR

This paper extends the Thomas-Fermi model to finite temperatures within General Relativity to study gravitational phase transitions in fermionic systems, revealing conditions under which collapse is prevented or leads to black hole formation.

## Contribution

It introduces a relativistic finite-temperature model for fermionic systems, analyzing the conditions for gravitational phase transitions and collapse prevention.

## Key findings

- Condensed phase emerges below a critical temperature for N < N_{OV}.
- Quantum mechanics prevents collapse in certain regimes.
- Systems with N > N_{OV} tend to collapse into black holes.

## Abstract

The Thomas-Fermi model is extended at finite temperature, to describe the gravitational phase transition occurring in massive fermionic systems in a general-relativistic framework. It is shown that, when a nondegenerate fermionic gas (for $N < N_{OV}$, where $N_{OV}$ is the Oppenheimer-Volkoff limit) is cooled down below a critical temperature, a condensed phase emerges and the gravitational collapse is prevented by quantum mechanics. If $N > N_{OV}$, by contrast, the system is destined to collapse towards a Black Hole because no equilibrium states exist.