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# Introduction

Brane world scenario has been discussed by many authors recently. The scenario suggests that the Planck energy can be as low as TeV scale [1]. If the Planck energy is TeV scale, it is possible to create black holes using accelerators, such as LHC [2]. Further, the collisions of cosmic rays with our atmosphere have energy reach beyond that of LHC and their observation will find the existence of the large extra-dimension or will place improved bounds on the fundamental Planck scale. Hence we would like to better understand the process of the black hole formation via particle collisions. For this purpose, we investigate the formation of the apparent horizon for the system of the head-on collisions of high-energy particles.

To simplify the analysis, we follows the method adopted by Eardley and Giddings [3]. First, the tension of the brane which is expected to be the Planck scale can be negligible if the center of mass energy is substantially larger than the Planck scale. Second, the geometry of the extra dimensions plays no essential role if the geometrical scales of the extra dimensions are large compared to the horizon radius for the center of mass energy. Thus we consider the head-on collisions in -dimensional Einstein gravity. The metric with a high-energy point particle is obtained by infinitely boosting the Schwarzschild black hole metric with the fixed total energy . The resulting system becomes a massless point particle accompanied by a plane-fronted gravitational shock wave which is the Lorentz-contracted longitudinal gravitational field of the particle. Combining two shock waves, we can set up the high energy collision. This system was originally developed by D'Eath and Payne [4]. The black hole formation with an impact parameter for was investigated by Eardley and Giddings [3], and they showed that the apparent horizon which encloses two particles exists at the instance of collision for sufficiently small impact parameter.

We examine the head-on collisions using the different slicing of the spacetime: we expect that the apparent horizon forms before the collision of two particles. We construct the solutions of the apparent horizons analytically and discuss how the dimension affects the formation of the horizon from the viewpoint of the hoop conjecture [5].

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