Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

Version 1 : Received: 28 July 2021 / Approved: 29 July 2021 / Online: 29 July 2021 (10:40:47 CEST)
Version 2 : Received: 31 July 2021 / Approved: 2 August 2021 / Online: 2 August 2021 (13:38:51 CEST)
Version 3 : Received: 24 August 2021 / Approved: 25 August 2021 / Online: 25 August 2021 (09:01:26 CEST)

A peer-reviewed article of this Preprint also exists.

Physics 2021, 3(3), 790-798; Physics 2021, 3(3), 790-798;


The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.


General relativity; Uncertainty principle; Geodesics; Black hole singularity; vacuum energy; Quantum gravity; Planck star


Physical Sciences, Quantum Science and Technology

Comments (1)

Comment 1
Received: 25 August 2021
Commenter: David Escors
Commenter's Conflict of Interests: Author
Comment: The manuscript underwent major revision after peer-review. It has substantially changed, and its quality significantly improved. The corrected manuscript will be sent for publication shortly.
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