On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes

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Hauptverfasser: Roy, Manali, Muthukumar, B.
Format: Preprint
Veröffentlicht: 2022
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author Roy, Manali
Muthukumar, B.
author_facet Roy, Manali
Muthukumar, B.
contents It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.
format Preprint
id arxiv_https___arxiv_org_abs_2205_02479
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
Roy, Manali
Muthukumar, B.
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Metric Geometry
It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.
title On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Metric Geometry
url https://arxiv.org/abs/2205.02479