Polymer quantization of the Einstein-Rosen wormhole throat

Abstract

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly-spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numerical accuracy, the area spectrum obtained from a Schrodinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.

21 pages, 8 figures. References added, minor typos corrected. Published version

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• Statistical Thermodynamics of Polymer Quantum Systems
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• Boundary conditions in quantum mechanics on the discretized half-line
• Polymer inflation
• Quantum dynamics of the Einstein-Rosen wormhole throat
• Instanton solutions on the polymer harmonic oscillator
• Quantum Effective Dynamics of Papapetrou Spacetime