: Received: 28 July 2021 / Approved: 29 July 2021 / Online: 29 July 2021 (10:40:47 CEST)
: Received: 31 July 2021 / Approved: 2 August 2021 / Online: 2 August 2021 (13:38:51 CEST)
: Received: 24 August 2021 / Approved: 25 August 2021 / Online: 25 August 2021 (09:01:26 CEST)
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, General & Theoretical Physics
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