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We consider generic nonextremal stationary dirty black holes. It is shownthat in the vicinity of any bifurcation surface the energy of collision of twoparticles in the centre of mass frame can grow unbound. This is a genericproperty that, in particular, includes collisions near the inner black holehorizon analyzed earlier by different methods. The similar results are alsovalid for cosmological horizons. The case of the de Sitter metric is discussed.

High energy particle collisions near the bifurcation surface