Critical formation of trapped surfaces in the collision of gravitational shock waves

TL;DR

This paper investigates the conditions under which trapped surfaces form during the collision of gravitational shock waves in various dimensions, revealing critical thresholds and scaling behaviors related to energy distribution.

Contribution

It identifies a critical spread of energy density affecting trapped surface formation and characterizes the associated scaling laws in different spacetime dimensions.

Findings

Existence of a critical energy spread in D=4 and D=5

Finite critical trapped surface size in D=4 at criticality

No critical threshold for D>5, always solutions exist

Abstract

We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space. For D=4 and D=5 it is shown that there exists a critical value of this spread above which no solution to the trapped surface equation is found. In four dimensions the trapped surface at criticality has a finite size, whereas in five the critical size vanishes. In both cases we find scaling relations characterized by critical exponents. Finally, when D>5 there is always a solution to the trapped surface equation for any transverse spread.