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Main Authors: Czuchry, Ewa, Gazeau, Jean-Pierre
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.13491
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author Czuchry, Ewa
Gazeau, Jean-Pierre
author_facet Czuchry, Ewa
Gazeau, Jean-Pierre
contents We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect. The regularized metric replaces $r^2$ by $r^2+σ^2$ in the angular part, where $σ$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2π$, independently of $σ$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $σ\to0$ leads to distributional Dirac-delta curvature and to appearance of topological defect at the origin. These results show that finite spatial resolution measurement does not merely smooth singularities but can shape spacetime geometry.
format Preprint
id arxiv_https___arxiv_org_abs_2601_13491
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Finite-resolution measurement induces topological curvature defects in spacetime
Czuchry, Ewa
Gazeau, Jean-Pierre
General Relativity and Quantum Cosmology
High Energy Physics - Theory
We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect. The regularized metric replaces $r^2$ by $r^2+σ^2$ in the angular part, where $σ$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2π$, independently of $σ$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $σ\to0$ leads to distributional Dirac-delta curvature and to appearance of topological defect at the origin. These results show that finite spatial resolution measurement does not merely smooth singularities but can shape spacetime geometry.
title Finite-resolution measurement induces topological curvature defects in spacetime
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2601.13491