Type IIB Colliding Plane Waves

TL;DR

This paper constructs and analyzes higher-dimensional colliding plane wave solutions in Einstein gravity with flux, revealing that small perturbations generally lead to curvature singularities, with specific relevance to ten-dimensional type IIB supergravity.

Contribution

It introduces exact higher-dimensional CPW solutions using an isomorphism with four-dimensional cases and studies their perturbations, extending classical solutions to higher dimensions.

Findings

Perturbations typically produce curvature singularities.

Higher-dimensional solutions analogous to known four-dimensional ones.

Relevance to ten-dimensional type IIB supergravity.

Abstract

Four-dimensional colliding plane wave (CPW) solutions have played an important role in understanding the classical non-linearities of Einstein's equations. In this note, we investigate CPW solutions in $2n+2$--dimensional Einstein gravity with a $n+1$-form flux. By using an isomorphism with the four-dimensional problem, we construct exact solutions analogous to the Szekeres vacuum solution in four dimensions. The higher-dimensional versions of the Khan-Penrose and Bell-Szekeres CPW solutions are studied perturbatively in the vicinity of the light-cone. We find that under small perturbations, a curvature singularity is generically produced, leading to both space-like and time-like singularities. For $n=4$, our results pertain to the collision of two ten-dimensional type IIB Blau - Figueroa o'Farrill - Hull - Papadopoulos plane waves.