# Particle collision with an arbitrarily high center-of-mass energy near a Ba\~nados-Teitelboim-Zanelli black hole

## TL;DR

This paper investigates conditions under which particle collisions near a BTZ black hole can achieve arbitrarily high center-of-mass energies, highlighting the role of critical angular momentum in such high-energy events.

## Contribution

It derives the conditions for arbitrarily high collision energies near a BTZ black hole, emphasizing the significance of critical angular momentum in these processes.

## Key findings

- Center-of-mass energy can be arbitrarily large at the horizon with critical angular momentum.
- Ingoing particles with critical and non-critical angular momentum can produce high-energy collisions.
- Subcritical angular momentum particles can approach the extremal BTZ black hole, enabling high-energy tail-on collisions.

## Abstract

We consider a particle collision with a high center-of-mass energy near a Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. We obtain the center-of-mass energy of two general colliding geodesic particles in the BTZ black hole spacetime. We show that the center-of-mass energy of two ingoing particles can be arbitrarily large on an event horizon if either of the two particles has a critical angular momentum and the other has a non-critical angular momentum. We also show that the motion of a particle with a subcritical angular momentum is allowed near an extremal rotating BTZ black hole and that a center-of-mass energy for a tail-on collision at a point can be arbitrarily large in a critical angular momentum limit.