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General Relativity and Quantum Cosmology

arXiv:2111.07731 (gr-qc)
[Submitted on 15 Nov 2021]

Title:Fuzzy Schwarzschild (2+1)-spacetime

Authors:David Viennot
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Abstract:We present a toy model of fuzzy Schwarzschild space slice (as a noncommutative manifold) which quantum mean values and quantum quasi-coherent states (states minimizing the quantum uncertainties) have properties close to the classical slice of the $(r,\theta)$ Schwarzschild coordinates (the so-called Flamm's paraboloid). This fuzzy Schwarzschild slice is built as a deformation of the noncommutative plane. Quantum time observables are introduced to add a time quantization in the model. We study the structure of the quasi-coherent state of the fuzzy Schwarzschild slice with respect to the quasi-coherent state and the deformation states of the noncommutative plane . The quantum dynamics of a fermion interacting with a fuzzy black hole described by the present model is studied. In particular we study the decoherence effects appearing in the neighborhood of the fuzzy event horizon. An extension of the model to describe a quantum wormhole is also proposed, where we show that fermions cross the wormhole not by traveling by its internal space but by quantum tunneling, in accordance with the non-traversable character of classical Einstein-Rosen bridges.
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:2111.07731 [gr-qc]
  (or arXiv:2111.07731v1 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.2111.07731
Journal reference: J. Math. Phys. 63, 082302 (2022)
Related DOI: https://doi.org/10.1063/5.0091364

Submission history

From: David Viennot [view email]
[v1] Mon, 15 Nov 2021 13:22:24 UTC (6,560 KB)
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