Near horizon geometry of extremal black holes and Banados-Silk-West effect

TL;DR

This paper investigates particle collisions near extremal Kerr black holes, showing that while the BSW effect predicts infinite energy, the near horizon geometry yields finite energy, clarifying the discrepancy between the two approaches.

Contribution

The study compares the BSW effect with near horizon geometry analysis, demonstrating finite collision energies and explaining their disagreement.

Findings

Center-of-mass energy is finite in near horizon extremal Kerr geometry.

Discrepancy between BSW effect and near horizon analysis is explained.

Near horizon geometry provides a consistent framework for particle collisions.

Abstract

Recently, Banados, Silk and West analyzed a collision of two particles near the horizon of the extremal Kerr black hole and demonstrated that the energy in the center-of-mass frame can be arbitrarily large provided the angular momentum of one of the colliding particles takes a special value. As is known, the vicinity of the extremal Kerr black hole horizon can be viewed as a complete vacuum spacetime in its own right. In this work, we consider a collision of two neutral particles within the context of the near horizon extremal Kerr geometry and demonstrate that the energy in the center-of-mass frame is finite for any admissible value of the particle parameters. An explanation of why the two approaches disagree on the Banados-Silk-West effect is given.