Plane waves in quantum gravity: breakdown of the classical spacetime

TL;DR

This paper develops a quantum model of plane gravitational waves, revealing that quantum fluctuations cause classical spacetime descriptions to break down near regions of null geodesic focusing.

Contribution

It introduces a constraint-free midisuperspace quantum model for plane waves and analyzes the limitations of classical descriptions due to quantum fluctuations.

Findings

Quantum fluctuations grow near geodesic focusing regions.

Classical spacetime approximation fails in high-fluctuation regions.

Coherent states do not always correspond to classical spacetimes.

Abstract

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees of freedom can be interpreted as an infinite and continuous set of annihilation and creation like variables. We also consider a simplified version of the model, in which the number of modes is restricted to a discrete set. In both cases, the quantization is achieved by introducing a Fock representation. We find regularized operators to represent the metric and discuss whether the coherent states of the quantum theory are peaked around classical spacetimes. It is shown that, although the expectation value of the metric on Killing orbits coincides with a classical solution, its relative fluctuations become significant when one approaches a region where null geodesics are focused. In that region, the spacetimes described by coherent states fail to admit an approximate classical description. This result applies as well to the vacuum of the theory.