Multi-Fibers Bundles as a new model for high-dimensional Spacetimes

TL;DR

This paper introduces a new geometric model using multi-fiber bundles to explore higher-dimensional spacetimes, potentially explaining dark matter, energy, and unifying gravity with quantum physics.

Contribution

It generalizes fiber bundle structures to include product fibers, enabling modeling of deviations from standard 4D general relativity and unification approaches.

Findings

Proposes a mathematical framework for higher-dimensional fibers.

Suggests potential applications to dark matter and energy modeling.

Lays groundwork for unifying gravity and quantum physics.

Abstract

Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string theory, suggest the need for a spacetime with more than five dimensions. We want to present in this paper a mathematical structure generalizing the fiber bundle structure to the case of a product fiber of the form $F=S \times W$, that enable the possible definition of multiple naturally defined fibers at each point of the manifold, on which therefore one can define objects that depend only on one of the components of the global fiber. Although we do not pretend here to model precisely other known physical interactions, we present this geometric structure as a possible way to model or encode deviations from standard 4-dimensional General Relativity, or "dark" effects such as dark matter or energy ; (we refer to the authors' article [3] ). Also this geometry was a starting point for the second author's new approach to a geometric unification of General Relativity and Quantum Physics ( see [23]).