Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

  • When minimal length uncertainty emerging from a generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on gravitational Einstein field equations (gEFEs) and to try to assess consequential modifications in metric manifesting properties of quantum geometry due to quantum gravity. GUP takes into account the gravitational impacts on the noncommutation relations of length (distance) and momentum operators or time and energy operators and so on. On the other hand, gEFE relates classical geometry or general relativity gravity to the energy–momentum tensors, that is, proposing quantum equations of state. Despite the technical difficulties, we intend to insert GUP into the metric tensor so that the line element and the geodesic equation in flat and curved space are accordingly modified. The latter apparently encompasses acceleration, jerk, and snap (jounce) of a particle in the quasi-quantized gravitational field. Finite higher orders of acceleration apparently manifest phenomena such as accelerating expansion and transitions between different radii of curvature and so on.
Author:Abdel Nasser TawfikORCiD, Abdel Magied Diab, Sameh Shenawy, Eiman Abou El Dahab
Parent Title (English):Astronomische Nachrichten = Astronomical notes
Publisher:Wiley-VCH Verl.
Place of publication:Berlin
Document Type:Article
Date of Publication (online):2021/01/24
Date of first Publication:2021/01/24
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/03/16
Tag:generalized uncertainty principle; geodesic equation; line element; metric tensor; noncommutative geometry; quantum gravity; relativity and gravitation
Page Number:4
First Page:54
Last Page:57
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
5 Naturwissenschaften und Mathematik / 52 Astronomie / 520 Astronomie und zugeordnete Wissenschaften
6 Technik, Medizin, angewandte Wissenschaften / 62 Ingenieurwissenschaften / 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
Licence (German):License LogoCreative Commons - Namensnennung 4.0