Consequences of minimal length discretization on line element, metric tensor, and geodesic equation. Issue 1 (24th January 2021)

• Record Type: Journal Article
• Authors: Tawfik, Abdel Nasser; Diab, Abdel Magied; Shenawy, Sameh; El Dahab, Eiman Abou
• Other Names: Zen Vasconcellos C.A. guestEditor.; Hess P.O. guestEditor.; Piccinelli G. guestEditor.; Vargas Magaña M. guestEditor.; Ureña-Lopez L. guestEditor.; González Felipe R. guestEditor.; Boller Th. guestEditor.; Gullberg S. guestEditor.
• Is Part Of: Astronomische Nachrichten. Volume 342:Issue 1/2(2021)
• Page Start: 54
• Page End: 57
• Publication Date: 2021-01-24
• Subjects: generalized uncertainty principle -- geodesic equation -- line element -- metric tensor -- noncommutative geometry -- quantum gravity -- relativity and gravitation; Astronomy -- Periodicals; 520.5
• DOI: 10.1002/asna.202113880
• Languages: English
• ISSNs: 0004-6337

Abstract

Abstract : 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.