High energy particle collisions and geometry of horizon

TL;DR

This paper demonstrates that in certain black hole horizons, particle collisions can achieve infinite energy in the center of mass frame without fine-tuning, due to geometric properties causing near-light speed approach.

Contribution

It provides a model-independent analysis showing infinite collision energy near horizons where $g_{\

Findings

Infinite $E_{c.m.}$ at horizons with $g_{\phi\phi} \rightarrow 0$

High-energy collisions occur between particles approaching at different angles

Results are consistent across various black hole models

Abstract

We consider collision of two geodesic particles near the horizon of such an axially symmetric black hole (rotating or static) that the metric coefficient $g_{\phi \phi }\rightarrow 0$ there. It is shown that (both for regular and singular horizons) the energy in the centre of mass frame $% E_{c.m.}$ is indefinitely large even without fine-tuning of particles' parameters. Kinematically, this is collision between two rapid particles that approach the horizon almost with the speed of light but at different angles. The latter is the reason why the relative velocity tends to that of light, hence to high $E_{c.m.}$. Our approach is model-independent. It relies on general properties of geometry and is insensitive to the details of material source that supports the geometies of the type under consideration. For several particular models (the stringy black hole, the Brans-Dicke analogue of the Schwarzschild metric and the Janis-Newman-Winicour one) we recover the results found in literature previously.