Arising of trapped surfaces with non-trivial topology from colliding shock waves

TL;DR

This paper investigates the formation of trapped surfaces with non-trivial topology during high-energy shock wave collisions in higher-dimensional spacetimes, revealing topology changes depending on the dimension and parameters involved.

Contribution

It demonstrates the emergence of trapped surfaces with non-trivial topology in five-dimensional collisions, extending understanding of black hole formation in higher dimensions.

Findings

Trapped surfaces with topology R x S1 x S1 can form in 5D collisions.

Lightlike limits cannot be extended inside ring singularities for D=4 and D>5.

A critical Kerr parameter a_c influences the formation of these surfaces.

Abstract

The lightlike limit of boosted black hole solutions with one angular momentum is considered for $D \geq4$ dimensions. The boost is performed parallel to the angular momentum and the lightlike limit is done by means of perturbative expansions. We shown that for $D=4$ and $D> 5$ the lightlike limit cannot be extended inside the ring singularity. Then, for $D = 5$ we discuss the arising of trapped surfaces in the head-on collision. We find that, inside the validity of the perturbative analysis we do, a trapped surface with topology $\mathbb R \times \mathbb S_1 \times\mathbb S_1$ seems to appear over the past light cone of the collision below a critical value $a_c$ of the Kerr parameter $a$.