Collision of high-energy closed strings: Formation of a ring-like apparent horizon

TL;DR

This paper investigates high-energy collisions of closed strings in higher-dimensional gravity, demonstrating that large ring radii can lead to the formation of ring-shaped apparent horizons, including black rings.

Contribution

The study introduces a model of high-energy closed strings as pp-waves with ring sources and numerically analyzes the formation of black hole and black ring apparent horizons.

Findings

Black ring apparent horizons form for sufficiently large ring radii.

Both black hole and black ring horizons can form depending on parameters.

Conditions for horizon formation are clarified in terms of ring radius R.

Abstract

We study collisions of two high-energy closed strings in the framework of $D$-dimensional general relativity. The model of a high-energy closed string is introduced as a {/it pp}-wave generated by a ring-shaped source with the radius $R$. At the instant of the collision, the positions of two strings are assumed to coincide precisely. In this setup, we study the formation of two kinds of apparent horizons (AHs): the AH of topology $S^{D-2}$ (the black hole AH) and the AH of topology $S^1/times S^{D-3}$ (the black ring AH). These two AHs are solved numerically and the conditions for the formation of the two AHs are clarified in terms of the ring radius $R$. Specifically, we demonstrate that the black ring AH forms for sufficiently large $R$. The effects of an impact parameter and the relative orientation of incoming strings in more general cases are briefly discussed.