Towards fractal gravity

TL;DR

This paper explores a theoretical model where fractal space-time variations are compensated by metric adjustments, suggesting a link between fractal topology and spacetime curvature, potentially offering new insights into gravity.

Contribution

It introduces a novel hypothesis that fractal space-time variations can be represented through metric changes, unifying fractal topology with classical continuum descriptions of gravity.

Findings

Fractal variations can be modeled as metric adjustments.

Topological gaps may induce spacetime curvature.

Intrinsic perception of fractal space appears classical.

Abstract

In an extension of speculations that physical space-time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to "compensate" for local variations of the fractal dimension by instead varying the metric in such a way that the intrinsic (as seen from an embedded observer) dimensionality remains an integer. Thereby, an extrinsic fractal continuum is intrinsically perceived as a classical continuum. Conversely, it is suggested that any variation of the metric from its Euclidean (or Minkowskian) form can be "shifted" to nontrivial fractal topology. Thereby "holes" or "gaps" in spacetime could give rise to (increased) curvature.