Ultrahigh energy particle collisions near many-dimensional black holes: general approach

If two particles moving towards a black hole collide near the horizon, their energy in the centre of mass frame can grow unbounded. This is the so-called Banados - Silk - West (BSW) effect. Earlier, it was shown that in the 3+1 space-time this effect has a universal nature. We show that for a wide class of many-dimensional black holes (including, say, the Myers-Perry black hole) this is also true. The suggested analysis is general and does not require special properties of the metric like separability of variables for geodesics, etc.