Quantum probing of null-singularities

TL;DR

This paper investigates quantum probes near null-singularities in plane-wave space-times using a dual-null foliation approach, revealing differences between Einstein-Rosen and Brinkmann patches and their gravitational memory effects.

Contribution

It introduces a dual-null foliation method in the quantum field theory context to analyze null-singularities and compares different spacetime patches to understand gravitational memory.

Findings

Einstein-Rosen space-times support configurations with non-empty gravitational memory.

Configurations in Einstein-Rosen are focused to a measure-zero set in the focal plane.

A framework is proposed to estimate back-reaction effects on these configurations.

Abstract

We adapt the dual-null foliation to the functional Schr\"odinger representation of quantum field theory and study the behavior of quantum probes in plane-wave space-times near the null-singularity. A comparison between the Einstein-Rosen and the Brinkmann patch, where the latter extends beyond the first, shows a seeming tension that can be resolved by comparing the configuration spaces. Our analysis concludes that Einstein-Rosen space-times support exclusively configurations with non-empty gravitational memory that are focussed to a set of measure zero in the focal plane with respect to a Brinkmann observer. To conclude, we provide a rough framework to estimate the qualitative influence of back-reactions on these results.