Motion and collision of particles in rotating linear dilaton black hole

TL;DR

This paper analyzes particle motion and high-energy collisions near a four-dimensional linear dilaton black hole, revealing it can act as a particle accelerator and comparing its behavior to the BTZ black hole.

Contribution

It provides an analytical solution for particle trajectories and demonstrates the black hole's ability to facilitate arbitrarily high-energy collisions via the BSW process.

Findings

Particles can reach the inner horizon with infinite CM energy.

Photon trajectories show they can either plunge or escape, with no confined orbits for massive particles.

The black hole's particle dynamics resemble those of the BTZ black hole.

Abstract

We study the motion of particles in the background of a four-dimensional linear dilaton black hole. We solve analytically the equations of motion of the test particles and we describe their motion. We show that the dilaton black hole acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon. In particular we find that there is a critical value of the angular momentum, which depends on the string coupling, and a particle with this critical angular momentum can reach the inner horizon with an arbitrarily high CM energy. This is known as the Ba\~nados, Silk and West (BSW) process. We also show that the motion and collisions of particles have a similar behavior to the three-dimensional BTZ black hole. In fact, the photons can plunge into the horizon or escape to infinity, and they can not be deflected, while for massive particles there are no confined orbits of first kind, like planetary or circular orbits.