A Theoretical Framework for Self-Gravitating k-Form Boson Stars with Internal Symmetries

TL;DR

This paper develops a comprehensive theoretical framework for self-gravitating bosonic fields with arbitrary antisymmetric tensor fields and internal gauge symmetries, extending current models to include higher-form fields and complex internal symmetries.

Contribution

It introduces a generalized formalism for k-form fields with gauge symmetries, deriving equations of motion and connection coefficients, applicable to models like pion condensates and dark matter.

Findings

Derived equations of motion for k-form fields with internal symmetries

Explicitly calculated connection coefficients for SU(2) in spherical symmetry

Presented a practical framework adaptable to various physical models

Abstract

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.