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We study high energy particle collisions around the higher dimensional blackholes. It is shown that the center of mass energy can be arbitrarily large inthe vicinity of the event horizon like the Banados, Silk and West (BSW) processin four dimensions if the following two conditions are satisfied: (i) thehorizon is extremal and (ii) the parameters of either of the two collidingparticles are fine-tuned, which is called a critical particle condition. Wealso show that a test particle which satisfies the critical particle conditioncan reach the event horizon from a distant region for a simple case. Finally,we discuss the relation between the BSW process and the linear instability oftest fields around the extremal black holes, the latter of which has beenrecently found by Aretakis.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

High Energy Collision of Particles in the Vicinity of Extremal Black  Holes in Higher Dimensions: Banados-Silk-West Process as Linear Instability  of Extremal Black Holes