English

Minimal length discretization and properties of modified metric tensor and geodesics

General Physics 2021-12-01 v2

Abstract

We argue that the minimal length discretization generalizing the Heisenberg uncertainty principle, in which the gravitational impacts on the non--commutation relations are thoughtfully taken into account, radically modifies the spacetime geometry. The resulting metric tensor and geodesic equation combine the general relativity terms with additional terms depending on higher--order derivatives. Suggesting solutions for the modified geodesics, for instance, isn't a trivial task. We discuss on the properties of the resulting metric tensor, line element, and geodesic equation.

Keywords

Cite

@article{arxiv.2111.05105,
  title  = {Minimal length discretization and properties of modified metric tensor and geodesics},
  author = {Abdel Nasser Tawfik and Fady T. Farouk and F. Salah Tarabia and Muhammad Maher},
  journal= {arXiv preprint arXiv:2111.05105},
  year   = {2021}
}

Comments

8 pages, no figure or table, an invited talk at Sixteenth Marcel Grossmann Meeting, accepted for publication in MG16 proceedings (some dummy variables are controlled)