Timescale for trans-Planckian collisions in Kerr spacetime

TL;DR

This paper compares the timescales of ultra-high energy particle collisions near extremal Kerr black holes and over-spinning Kerr singularities, finding that over-spinning cases allow for observable Planck-scale collisions within cosmic timescales.

Contribution

It provides a detailed analysis of collision timescales in Kerr spacetimes, highlighting the observational advantages of over-spinning Kerr geometries for Planck-scale physics.

Findings

Collision times near extremal Kerr black holes exceed the age of the universe.

Over-spinning Kerr singularities enable collisions within about ten million years.

Over-spinning Kerr geometry offers better prospects for observing Planck-scale phenomena.

Abstract

We make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.