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Gravity model for topological features on a cylindrical manifold

Igor Bayak
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Abstract

A model aimed at understanding quantum gravity in terms of Birkhoff's approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a $\mathbb{R}^{3} \times S^{1}$-cylinder. The basic field of this model is a field of unit vectors defined through the velocity field of a flow wrapping the cylinder. The degeneration of some parts of the flow into circles (topological features) results in inhomogeneities and gives rise to a scalar field, analogous to the gravitational field. The geometry and dynamics of this field are briefly discussed. We treat the intersections between the topological features and the observer's 3-space as matter particles and argue that these entities are likely to possess some quantum properties.

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Igor Bayak. 2007-06-20. Gravity model for topological features on a cylindrical manifold. https://arxiv.org/abs/math/0603536

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