Large quantum gravity effects: Cylindrical waves in four dimensions

TL;DR

This paper develops a complete quantum theory for four-dimensional Einstein-Rosen waves, revealing significant quantum gravity effects and analyzing metric fluctuations, with implications for classical and quantum descriptions of cylindrical gravitational waves.

Contribution

It extends Ashtekar and Pierri's quantization to a full four-dimensional framework, constructing regularized metric operators and analyzing quantum effects and fluctuations.

Findings

Quantum gravity effects persist at large distances from the axis.

Coherent Maxwell states do not require many photons for classical behavior.

Metric fluctuations are significant across all coherent states.

Abstract

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein-Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein-Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein-Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.