# Analysis Seminar

#### Impulsive Gravitational Waves

**Speaker:**
Jonathan Luk, Princeton University

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, December 6, 2012, 11 a.m.

**Synopsis:**

We study the problem of the propagation and nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations. The problem is studied in the context of a characteristic initial value problem with data given on two null hypersurfaces and containing curvature delta singularities. For a single impulsive gravitational wave, we show that in the resulting spacetime, the delta singularity propagates along a 3-dimensional characteristic hypersurface, while away from that hypersurface the spacetime remains smooth. We also construct spacetimes representing interaction of two impulsive gravitational waves in which the curvature delta singularities propagate along two 3-dimensional null hypersurfaces intersecting to the future of the data. To the past of the intersection, the spacetime can be thought of as containing two independent, non-interacting impulsive gravitational waves and the intersection represents the first instance of their nonlinear interaction. Our analysis extends to the region past their first interaction and shows that the spacetime still remains smooth away from the continuing propagating individual waves. This is joint work with Igor Rodnianski.