  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.
