Critical Trapped Surfaces Formation in the Collision of Ultrarelativistic Charges in (A)dS

TL;DR

This paper investigates the conditions under which trapped surfaces form during ultrarelativistic charge collisions in (A)dS space-times, revealing critical charge values and the influence of cosmological constants on trapped surface formation.

Contribution

It introduces a detailed analysis of critical charge thresholds for trapped surface formation in (A)dS spaces, extending previous Minkowski space results to curved backgrounds.

Findings

Trapped surface formation depends on charge, energy, and cosmological constant.

Critical charge values determine the possibility of trapped surface formation.

In (A)dS space, small nonzero charges can prevent trapped surface formation.

Abstract

We study the formation of marginally trapped surfaces in the head-on collision of two ultrarelativistic charges in $(A)dS$ space-time. The metric of ultrarelativistic charged particles in $(A)dS$ is obtained by boosting Reissner-Nordstr\"om $(A)dS$ space-time to the speed of light. We show that formation of trapped surfaces on the past light cone is only possible when charge is below certain critical - situation similar to the collision of two ultrarelativistic charges in Minkowski space-time. This critical value depends on the energy of colliding particles and the value of a cosmological constant. There is richer structure of critical domains in $dS$ case. In this case already for chargeless particles there is a critical value of the cosmological constant only below which trapped surfaces formation is possible. Appearance of arbitrary small nonzero charge significantly changes the physical picture. Critical effect which has been observed in the neutral case does not take place more. If the value of the charge is not very large solution to the equation on trapped surface exists for any values of cosmological radius and energy density of shock waves. Increasing of the charge leads to decrease of the trapped surface area, and at some critical point the formation of trapped surfaces of the type mentioned above becomes impossible.