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

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

2010-10-26

arxiv.org/abs/1010.5438v2

Phys.Rev.D83:044013,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 2 figures, title changed

Scientific paper

10.1103/PhysRevD.83.044013

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.

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