Black hole formation in the grazing collision of high-energy particles

TL;DR

This paper numerically studies black hole formation in high-energy particle collisions in higher dimensions, identifying conditions for apparent horizon formation based on impact parameter and geometric measures.

Contribution

It introduces a numerical method to evaluate black hole formation in high-dimensional collisions and compares geometric criteria for horizon formation.

Findings

Apparent horizon forms when particles are within 1.5 times the gravitational radius.

(D-3)-dimensional volume is a better predictor for horizon formation than the hoop conjecture.

Numerical results support higher-dimensional geometric criteria for black hole formation.

Abstract

We numerically investigate the formation of D-dimensional black holes in high-energy particle collision with the impact parameter and evaluate the total cross section of the black hole production. We find that the formation of an apparent horizon occurs when the distance between the colliding particles is less than 1.5 times the effective gravitational radius of each particles. Our numerical result indicates that although both the one-dimensional hoop and the (D-3)-dimensional volume corresponding to the typical scale of the system give a fairly good condition for the horizon formation in the higher-dimensional gravity, the (D-3)-dimensional volume provide a better condition to judge the existence of the horizon.