Type-IIB colliding plane waves

Four-dimensional colliding plane wave (CPW) solutions have played animportant role in understanding the classical non-linearities of Einstein'sequations. In this note, we investigate CPW solutions in $2n+2$--dimensionalEinstein gravity with a $n+1$-form flux. By using an isomorphism with thefour-dimensional problem, we construct exact solutions analogous to theSzekeres vacuum solution in four dimensions. The higher-dimensional versions ofthe Khan-Penrose and Bell-Szekeres CPW solutions are studied perturbatively inthe vicinity of the light-cone. We find that under small perturbations, acurvature singularity is generically produced, leading to both space-like andtime-like singularities. For $n=4$, our results pertain to the collision of twoten-dimensional type IIB Blau - Figueroa o'Farrill - Hull - Papadopoulos planewaves.Comment: 20+10 pages, 2 figures, uses JHEP3.cls; v2: refs [3,10,22] corrected, remark added below (3.9) on inexistence of conformally flat CPW in our ansatz, final version to appear in JHE