Plane waves with weak singularities

TL;DR

This paper investigates a class of vacuum Einstein plane wave solutions with weak null singularities, demonstrating that string theory can smoothly propagate through these singularities and proposing a method to resolve them.

Contribution

It introduces a subclass of weak singular plane waves where string propagation remains well-defined and constructs a family of smooth metrics to resolve the singularity.

Findings

String propagation is smooth in these backgrounds.

A natural extension of the metric beyond the singularity is possible.

A family of smooth metrics resolves the singularity in string theory.

Abstract

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which do not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity.