Acceleration of colliding shells around a black hole: Validity of the test particle approximation in the Banados-Silk-West process

TL;DR

This paper investigates the validity of the test particle approximation in the BSW process near black holes by analyzing colliding spherical shells, showing that their own gravity imposes an upper energy limit.

Contribution

It demonstrates that the gravitational effects of colliding shells limit the energy achievable in the BSW process, challenging the assumption of test particles in extreme black hole collisions.

Findings

Energy of colliding shells has an upper limit due to their gravity.

The upper limit suggests similar constraints for colliding particles in the BSW process.

Gravity effects cannot be neglected in high-energy black hole collision scenarios.

Abstract

Recently, Banados, Silk and West (BSW) showed that the total energy of two colliding test particles has no upper limit in their center of mass frame in the neighborhood of an extreme Kerr black hole, even if these particles were at rest at infinity in the infinite past. We call this mechanism the BSW mechanism or BSW process. The large energy of such particles would generate strong gravity, although this has not been taken into account in the BSW analysis. A similar mechanism is seen in the collision of two spherical test shells in the neighborhood of an extreme Reissner-Nordstr\"om black hole. In this paper, in order to draw some implications concerning the effects of gravity generated by colliding particles in the BSW process, we study a collision of two spherical dust shells, since their gravity can be exactly treated. We show that the energy of two colliding shells in the center of mass frame observable from infinity has an upper limit due to their own gravity. Our result suggests that an upper limit also exists for the total energy of colliding particles in the center of mass frame in the observable domain in the BSW process due the gravity of the particles.