Type IIB Colliding Plane Waves

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.