Midi-Superspace Quantization of Non-Compact Toroidally Symmetric Gravity

TL;DR

This paper develops a quantization approach for a class of non-compact, toroidally symmetric spacetimes, revealing significant quantum dispersive effects in their asymptotic regions.

Contribution

It introduces a simplified quantization method for non-compact toroidally symmetric gravity, extending midi-superspace models beyond compact Gowdy spacetimes.

Findings

Quantum geometry exhibits large dispersive effects

Classical phase space reduces to a free scalar field

Non-perturbative quantum features analyzed

Abstract

We consider the quantization of the midi-superspace associated with a class of spacetimes with toroidal isometries, but without the compact spatial hypersurfaces of the well-known Gowdy models. By a symmetry reduction, the phase space for the system at the classical level can be identified with that of a free massless scalar field on a fixed background spacetime, thereby providing a simple route to quantization. We are then able to study certain non-perturbative features of the quantum gravitational system. In particular, we examine the quantum geometry of the asymptotic regions of the spacetimes involved and find some surprisingly large dispersive effects of quantum gravity.