Version 1
: Received: 6 June 2023 / Approved: 7 June 2023 / Online: 7 June 2023 (11:06:17 CEST)
How to cite:
Maher, M.; Tawfik, A. N.; Tarabia, F. S.; Farouk, F. T. Minimal Length Deformation of Spacetime Curvature. Preprints2023, 2023060543. https://doi.org/10.20944/preprints202306.0543.v1
Maher, M.; Tawfik, A. N.; Tarabia, F. S.; Farouk, F. T. Minimal Length Deformation of Spacetime Curvature. Preprints 2023, 2023060543. https://doi.org/10.20944/preprints202306.0543.v1
Maher, M.; Tawfik, A. N.; Tarabia, F. S.; Farouk, F. T. Minimal Length Deformation of Spacetime Curvature. Preprints2023, 2023060543. https://doi.org/10.20944/preprints202306.0543.v1
APA Style
Maher, M., Tawfik, A. N., Tarabia, F. S., & Farouk, F. T. (2023). Minimal Length Deformation of Spacetime Curvature. Preprints. https://doi.org/10.20944/preprints202306.0543.v1
Chicago/Turabian Style
Maher, M., Fawzy Salah Tarabia and Fady Tarek Farouk. 2023 "Minimal Length Deformation of Spacetime Curvature" Preprints. https://doi.org/10.20944/preprints202306.0543.v1
Abstract
When generalized noncommutative Heisenberg algebra accommodating impacts of finite gravitational fields as specified by loop quantum gravity, doubly–special relativity, and string theory, for instance, is thoughtfully applied to the eight-dimensional manifold (M8), the generalization of the Riemannian manifold becomes imminent. By constructing the deformed affine connections on a four-dimensional Riemannian manifold, we have determined the minimal length deformation of Riemann curvature tensor and its contractions, the Ricci curvature tensor, and Ricci scalar. Consequently, we have been able to construct the deformed Einstein tensor. As in Einstein’s classical theory of general relativity, we have proved that the covariant derivative of the deformed Einstein tensor vanishes, as well. We conclude that the minimal length correction suggests a correction to the spacetime curvature which is manifest in the additional curvature terms of the corrected Riemann tensor and its contractions. Accordingly, the spacetime curvature endows additional curvature and geometrical structure.
Keywords
Deformed theories of gravity; Noncommutative geometry; Curved spacetime; Relativity and gravitation; Deformed Spacetime Curvature
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
