Minimal length discretization and properties of modified metric tensor and geodesics

Abdel Nasser Tawfik; Fady T. Farouk; F. Salah Tarabia; Muhammad Maher

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arXiv · 2111.05105

Minimal length discretization and properties of modified metric tensor and geodesics

Abdel Nasser Tawfik·Fady T. Farouk·F. Salah Tarabia·Muhammad Maher

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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.

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Abdel Nasser Tawfik, Fady T. Farouk, F. Salah Tarabia, Muhammad Maher. 2021-11-04. Minimal length discretization and properties of modified metric tensor and geodesics. https://arxiv.org/abs/2111.05105

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