Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Four Spacetime Dimensions from Multifractal Geometry

Version 1 : Received: 25 April 2021 / Approved: 26 April 2021 / Online: 26 April 2021 (10:56:12 CEST)

How to cite: Goldfain, E. Four Spacetime Dimensions from Multifractal Geometry. Preprints 2021, 2021040654 (doi: 10.20944/preprints202104.0654.v1). Goldfain, E. Four Spacetime Dimensions from Multifractal Geometry. Preprints 2021, 2021040654 (doi: 10.20944/preprints202104.0654.v1).

Abstract

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

Subject Areas

Multifractals, measure theory, Rényi entropy, generalized dimension, geodesic trajectories, relativistic spacetime.

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