Two gravitational shock waves on the AdS_3 brane

Abstract

A gravitational shock wave is a solution to Einstein equations describing the gravitational field of a massless particle. We obtain such a geometry for a particle moving on a AdS_3 brane embedded in a AdS_4 bulk (the lower dimensional version of the "locally localized gravity" model of Karch and Randall). In order to do this, we use two different techniques. First, we solve directly Einstein equations sourced by a massless particle. Then we boost to the speed of light the AdS_3 brane black hole solution of Emparan et al while sending its mass parameter to zero. Surprisingly, we obtain two different results. We discuss the origin of these two different solutions both in the bulk and in the CFT picture. As a by-product, we derive the expression for the shock wave associated to a transversally accelerating particle in AdS_4.