[Paper Review] Acceleration of colliding shells around a black hole -- Validity of test particle approximation in BSW process

Masashi Kimura, Ken-ichi Nakao+1 more|arXiv (Cornell University)|Oct 26, 2010

Astrophysical Phenomena and Observations3 citations

TL;DR

This paper investigates the validity of the test particle approximation in the BSW process by modeling colliding dust shells around an extreme black hole, showing that their self-gravity imposes an upper limit on the center-of-mass energy observable from infinity, implying a physical bound on the energy in the BSW mechanism due to particle-generated gravity.

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-Nordstrom 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.

Motivation & Objective

• To assess the validity of the test particle approximation in the BSW process, where infinite center-of-mass energy is predicted near extreme Kerr black holes.
• To investigate whether the gravity generated by colliding particles imposes a physical upper limit on the total collision energy.
• To model the collision of two spherical dust shells, allowing exact treatment of their self-gravity, as a more realistic alternative to test particle models.
• To determine whether the observable center-of-mass energy of colliding shells remains finite despite the BSW mechanism's prediction of unbounded energy.

Proposed method

• Model two spherical dust shells collapsing toward an extreme Reissner-Nordström black hole, using exact solutions of Einstein's equations for dust shells.
• Apply the junction conditions across the shell surfaces to derive the dynamics of the shells and their collision.
• Compute the center-of-mass energy in the local rest frame of the colliding shells, then transform it to the energy observed at infinity.
• Analyze the behavior of the center-of-mass energy as the shells approach the horizon, focusing on the role of their self-gravity.
• Compare the results with the BSW prediction for test particles to assess the impact of particle-generated gravity.

Experimental results

Research questions

• RQ1 Does the self-gravity of colliding particles in the BSW process impose a finite upper bound on the center-of-mass energy observable from infinity?
• RQ2 How does the energy of colliding dust shells in the center-of-mass frame behave near an extreme black hole when their own gravity is included?
• RQ3 To what extent does the test particle approximation fail in the BSW process due to the neglect of particle-generated gravitational fields?
• RQ4 Can the collision energy remain unbounded in the observable domain when the gravitational effects of the colliding shells are accounted for?

Key findings

• The center-of-mass energy of two colliding dust shells, as measured from infinity, is bounded from above due to their self-gravity.
• The upper limit on the observable center-of-mass energy arises from the backreaction of the shells' gravitational fields on their dynamics and collision.
• The result implies that the BSW mechanism's prediction of infinite energy is invalidated in a fully self-consistent gravitational model.
• The finite upper bound on energy is a direct consequence of the shells' mass and the curvature they generate, which prevents infinite energy accumulation.