The stability of Killing-Cauchy horizons in colliding plane wave space-times

TL;DR

This paper rigorously confirms that Killing-Cauchy horizons in colliding plane gravitational wave space-times are unstable under bounded perturbations of initial waves, specifically for constant aligned polarization cases.

Contribution

It provides a rigorous proof of the instability of Killing-Cauchy horizons in colliding plane wave space-times with aligned polarization.

Findings

Killing-Cauchy horizons are unstable under bounded perturbations.

The instability is confirmed specifically for constant aligned polarization.

The result applies to space-times modeling colliding plane gravitational waves.

Abstract

It is confirmed rigorously that the Killing-Cauchy horizons, which sometimes occur in space-times representing the collision and subsequent interaction of plane gravitational waves in a Minkowski background, are unstable with respect to bounded perturbations of the initial waves, at least for the case in which the initial waves have constant aligned polarizations.