Polymer quantization of the Einstein-Rosen wormhole throat

TL;DR

This paper develops a polymer quantization approach for the Einstein-Rosen wormhole throat, revealing a discrete area spectrum and replacing the classical singularity with a quantum bounce, advancing understanding of quantum gravity effects.

Contribution

It introduces a polymer quantization of the wormhole throat area, demonstrating a discrete spectrum and singularity resolution in quantum gravity context.

Findings

Area spectrum is evenly spaced and matches semiclassical estimates.

Singularity is replaced by a bounce at a scale-dependent radius.

Small polymerization scale recovers Schrödinger quantization results.

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.