Two gravitational shock waves on the AdS_3 brane

TL;DR

This paper constructs gravitational shock wave solutions for a massless particle on an AdS_3 brane within AdS_4, revealing two distinct solutions and exploring their physical implications.

Contribution

It introduces two different methods to derive shock wave geometries on an AdS_3 brane in AdS_4 and analyzes their differences and origins.

Findings

Two distinct shock wave solutions were obtained.

The solutions' differences are explained via bulk and CFT perspectives.

Derived the shock wave for a transversally accelerating particle in AdS_4.

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.