2024/05/13 by Jakob Hoffmann, Hoffmann, Jakob, Cédric Jockel +1
Mathematics · Physics and Astronomy · #Astrophysics #Boson #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Homogeneous space #Mathematical Physics (math-ph) #Mathematics #Particle physics #Physics #Pulsars and Gravitational Waves Research #Stars #Stellar, planetary, and galactic studies #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2405.08178
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Current boson star models are largely restricted to global symmetries and lower spin fields. In this work, we generalize these systems of self-gravitating bosonic fields to allow for arbitrary totally antisymmetric tensor fields and arbitrary internal gauge symmetries. We construct a generalized formalism for Yang-Mills-like theories, which allows for arbitrary k-form fields, instead of just vector fields. The k-form fields have gauge symmetries described by semisimple, compact Lie groups. We further derive equations of motion for the k-form fields and connection coefficients of the Lie group. Extensions and applications are also discussed. We present a novel way to fix the group connection using a spacetime connection. As an example, we derive explicitly the connection coefficients for SU(2) in a spherically symmetric spacetime using rectangular vielbeins. The combination of methods presented leads to a powerful, adaptable and practical framework. As a proof of concept, we derive ordinary differential equations for a 0-form field with a SU(2) symmetry. Our framework can be used to model self-gravitating (multi) particle states with internal symmetries, such as pion condensates or dark matter. It is also suited as a tool to approach open problems in modified gravity and string theory.