arXiv:2508.11714v1 Announce Type: new
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.
Future Roadmap
Based on the conclusions of the study, readers can look forward to the following opportunities and challenges in the field of self-gravitating Dirac fields with scalar fermion interactions:
Opportunities:
- Exploration of soliton solutions consisting of two fermions with strong attractive self-interaction.
- Potential for soliton solutions to exceed the Arnowitt-Deser-Misner mass limit of noninteracting Dirac stars.
- Discovery of multiple valid “particle-like” solutions for a single set of parameters, showcasing the nonlinear nature of the Dirac field.
- Mass-scale separation phenomenon similar to the Einstein-Dirac-Higgs system, offering insights into the behavior of the system.
- Possibility of studying parity-violated solutions and their restoration by increasing the central redshift of the solution.
Challenges:
- Verification of theoretical predictions through experimental observations or simulations.
- Understanding the underlying mechanisms that allow soliton solutions to exceed mass limits and exhibit multiplicity.
- Investigating the implications of mass-scale separation on the overall dynamics of the system.
- Exploring the practical applications of parity-violated solutions and their restoration in real-world scenarios.
Overall, the future roadmap for researchers in this field involves delving deeper into the implications of the study’s conclusions, addressing the challenges posed, and leveraging the opportunities presented to further our understanding of self-gravitating Dirac fields with scalar fermion interactions.