Self-gravitating nonlinear Dirac fields

TL;DR

This paper investigates self-gravitating nonlinear Dirac fields with scalar self-interaction, revealing that strong interactions can produce more massive soliton solutions, multiple solutions for the same parameters, and parity-violated states that can be restored.

Contribution

It introduces the effects of scalar self-interaction on Dirac fields coupled to gravity, showing enhanced mass limits, solution multiplicity, and parity violation phenomena.

Findings

Maximum mass of solutions exceeds noninteracting limits with strong self-interaction

Multiple solutions exist for the same parameters due to nonlinearity

Parity violation occurs and can be restored by increasing central redshift

Abstract

We consider the self-gravitating Dirac field with a scalar fermion self-interaction term. For strong enough attractive fermion self-interaction, the maximum Arnowitt-Deser-Misner mass of soliton solutions consisting of two fermions can exceed the limit of noninteracting Dirac stars classically, and the "particle-like" solutions of the system can exhibit multiplicity, multiple valid solutions for a single set of parameters, that is inherent in the nonlinear Dirac field. We also find the mass-scale separation in our system similar to that discussed in the Einstein-Dirac-Higgs system. Interestingly, the system admits parity-violated solutions. The broken parity symmetry can be restored by increasing the central redshift of the solution.