Particle Acceleration in Kerr-(anti-) de Sitter Black Hole Backgrounds

TL;DR

This paper extends the analysis of particle collisions near Kerr black holes to include spacetimes with nonzero cosmological constants, revealing conditions under which arbitrarily high energies can occur.

Contribution

It investigates particle acceleration in Kerr-(anti-) de Sitter black holes, showing how the cosmological constant affects the feasibility of infinite energy collisions.

Findings

High-energy collisions possible in Kerr-de Sitter black holes regardless of extremality.

Only extremal Kerr-anti-de Sitter black holes allow unbounded collision energies without fine tuning.

Potential to tune particle angular momentum for high-energy collisions without increasing particle energy.

Abstract

Recently, Ban\~{a}dos, Silk and West (BSW) found that the center-of-mass energy of two colliding test particles in the neighborhood of an extreme Kerr black hole could be arbitrarily high when one particle has the critical angular momentum $L_\text{C}$. In their paper, they considered the black holes living in a Minkowski space-time with a zero cosmological constant. In this work, we study this process of particles in the backgrounds of the Kerr black holes living in a space-time with a nonzero cosmological constant. We find that for kerr black holes living in a space-time with a negative cosmological constant (Kerr-anti-de Sitter black holes), this process of particles could happen only if the Kerr-anti-de Sitter black hole is extreme and an additional fine tuning is satisfied; while for kerr black holes living in a space-time with a positive cosmological constant (Kerr-de Sitter black holes), this process of particles could happen no matter the Kerr-de Sitter black hole is extreme or not. We also study the particle collision outside the outer horizon of the Kerr-(anti-) de Sitter black hole in some cases. We find that there is a possibility that we could tune one colliding particle's angular momentum to gain the large center-of-mass energy without increase the particle's energy.