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Recently, Banados, Silk and West analyzed a collision of two particles nearthe horizon of the extremal Kerr black hole and demonstrated that the energy inthe center-of-mass frame can be arbitrarily large provided the angular momentumof one of the colliding particles takes a special value. As is known, thevicinity of the extremal Kerr black hole horizon can be viewed as a completevacuum spacetime in its own right. In this work, we consider a collision of twoneutral particles within the context of the near horizon extremal Kerr geometryand demonstrate that the energy in the center-of-mass frame is finite for anyadmissible value of the particle parameters. An explanation of why the twoapproaches disagree on the Banados-Silk-West effect is given.

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