Minimal length discretization and properties of modified metric tensor\n and geodesics

2021/11/04 by Abdel Nasser Tawfik, Fady T. Farouk, Tawfik, Abdel Nasser +5 · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Pulsars and Gravitational Waves Research

paper · pdf · doi:10.48550/arxiv.2111.05105

openalex publication_date 2021/11/04 · openalex created_date 2022/11/08 · openalex updated_date 2026/07/28

Abstract

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

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• Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution

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