Charged Spinning Black Holes as Particle Accelerators

TL;DR

This paper extends the concept of black holes as particle accelerators to charged spinning Kerr-Newman black holes, showing conditions for arbitrarily high collision energies depend on charge, spin, and extremality.

Contribution

It generalizes previous results by including charge, revealing new conditions for infinite energy collisions in Kerr-Newman black holes.

Findings

Unbounded collision energy occurs at extremal black hole horizons.

High energy collisions require specific angular momentum of particles.

Charge reduces the maximum achievable collision energy in near-extremal black holes.

Abstract

It has recently been pointed out that the spinning Kerr black hole with maximal spin could act as a particle collider with arbitrarily high center-of-mass energy. In this paper, we will extend the result to the charged spinning black hole, the Kerr-Newman black hole. The center-of-mass energy of collision for two uncharged particles falling freely from rest at infinity depends not only on the spin $a$ but also on the charge $Q$ of the black hole. We find that an unlimited center-of-mass energy can be approached with the conditions: (1) the collision takes place at the horizon of an extremal black hole; (2) one of the colliding particles has critical angular momentum; (3) the spin $a$ of the extremal black hole satisfies $\frac{1}{\sqrt{3}}\leq \frac{a}{M}\leq 1$, where $M$ is the mass of the Kerr-Newman black hole. The third condition implies that to obtain an arbitrarily high energy, the extremal Kerr-Newman black hole must have a large value of spin, which is a significant difference between the Kerr and Kerr-Newman black holes. Furthermore, we also show that, for a near-extremal black hole, there always exists a finite upper bound for center-of-mass energy, which decreases with the increase of the charge $Q$.