Colliding AdS gravitational shock waves in various dimensions and holography

TL;DR

This paper numerically investigates the formation of trapped surfaces in off-center shock wave collisions in various AdS dimensions, revealing a critical impact parameter and a scaling relation, with implications for holographic duals.

Contribution

It introduces a numerical study of marginally trapped surface formation in off-center AdS shock wave collisions across multiple dimensions, linking gravitational dynamics to holography.

Findings

Existence of a critical impact parameter for trapped surface formation.

A simple scaling relation between critical impact parameter and energy.

Relation of solutions to holographic impact parameter scenarios.

Abstract

The formation of marginally trapped surfaces in the off-center collision of two shock waves on AdS_D (with D=4,5,6,7 and 8) is studied numerically. We focus on the case when the two waves collide with nonvanishing impact parameter while the sources are located at the same value of the holographic coordinate. In all cases a critical value of the impact parameter is found above which no trapped surface is formed. The numerical results show the existence of a simple scaling relation between the critical impact parameter and the energy of the colliding waves. Using the isometries of AdS_D we relate the solutions obtained to the ones describing the collision of two waves with a purely holographic impact parameter. This provides a gravitational dual for the head-on collision of two lumps of energy of unequal size.