Do spikes persist in a quantum treatment of spacetime singularities?

Ewa Czuchry, David Garfinkle, John R. Klauder, and Włodzimierz Piechocki
Phys. Rev. D 95, 024014 – Published 12 January 2017

Abstract

The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial point essentially becomes uncoupled from its neighbors. This uncoupled dynamics leads to sharp features (called “spikes”) as follows: particular spatial points follow an exceptional dynamical path that differs from that of their neighbors, with the consequence that, in the neighborhood of these exceptional points, the spatial profile becomes ever more sharp. Spikes are consequences of the BKL-type oscillatory evolution towards generic singularities of spacetime. Do spikes persist when the spacetime dynamics is treated using quantum mechanics? To address this question, we treat a Hamiltonian system that describes the dynamics of the approach to the singularity and consider how to quantize that system. We argue that this particular system is best treated using an affine quantization approach (rather than the more familiar methods of canonical quantization), and we set up the formalism needed for this treatment. Our investigation, based on this affine approach, shows the nonexistence of quantum spikes.

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  • Received 1 June 2016

DOI:https://doi.org/10.1103/PhysRevD.95.024014

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Ewa Czuchry1,*, David Garfinkle2,3,†, John R. Klauder4,‡, and Włodzimierz Piechocki1,§

  • 1Department of Fundamental Research, National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa, Poland
  • 2Department of Physics, Oakland University, Rochester, Michigan 48309, USA
  • 3Michigan Center for Theoretical Physics, Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA
  • 4Department of Physics and Department of Mathematics, University of Florida, Gainesville, Florida 32611-8440, USA

  • *ewa.czuchry@ncbj.gov.pl
  • garfinkl@oakland.edu
  • john.klauder@gmail.com
  • §wlodzimierz.piechocki@ncbj.gov.pl

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Issue

Vol. 95, Iss. 2 — 15 January 2017

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