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Free keywords:
General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
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.
