TY  - JOUR
A1  - Tawfik, Abdel Nasser
A1  - Diab, Abdel Magied
A1  - Shenawy, Sameh
A1  - Dahab, Eiman Abou El
T1  - Consequences of minimal length discretization on line element, metric tensor, and geodesic equation
T2  - Astronomische Nachrichten = Astronomical notes
N2  - 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.
KW  - generalized uncertainty principle
KW  - geodesic equation
KW  - line element
KW  - metric tensor
KW  - noncommutative geometry
KW  - quantum gravity
KW  - relativity and gravitation
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63879
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-638792
SN  - 1521-3994
VL  - 342
IS  - 1-2
SP  - 54
EP  - 57
PB  - Wiley-VCH Verl.
CY  - Berlin
ER  -