Perturbing the ground state of Dirac stars

TL;DR

This paper investigates the stability and dynamical behavior of Dirac stars, self-gravitating fermionic configurations, revealing stable and unstable branches and their evolution under perturbations, including collapse to black holes.

Contribution

It provides the first detailed dynamical stability analysis of Dirac stars, identifying conditions for stability, migration, and collapse, extending understanding beyond static solutions.

Findings

Existence of stable and unstable solution branches.

Unstable Dirac stars migrate to stable branches under perturbations.

Strong perturbations can cause collapse into black holes.

Abstract

Dirac stars are self-gravitating configurations of spin-1/2 fermions in which the fermions are described by the Dirac equation. After a detailed review of the derivation of the equations and their static solutions, we present an in-depth dynamical stability analysis of the ground state similar to previous studies for boson stars. We confirm that there exist both stable and unstable branches of static solutions and show that weakly perturbed Dirac stars from the unstable branch migrate to the stable branch. We also show that strongly perturbed Dirac stars from the stable branch migrate to the stable branch if their mass is below a critical value. If their mass is above the critical value they can migrate to the stable branch or collapse and form a black hole. For strongly perturbed Dirac stars from the unstable branch we show that the addition of even a small amount of mass leads to collapse, while if we decrease their mass they migrate to the stable branch.