Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

Abstract

The classical uncertainty principle inequalities were imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle was reformulated in terms of proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This reformulation confirmed the need for a minimum length of space-time line element in the geodesic, which depended on a Lorentz-covariant geodesic-derived scalar. In agreement with quantum gravity theories, GeUP imposed 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.

arXiv commentThe link to the published paper is: https://www.mdpi.com/2624-8174/3/3/49/htm

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Cited by in corpus (1)

• Covariant Space Time Line Elements in the Friedmann Lemaitre Robertson Walker Geometry