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We consider collision of two geodesic particles near the horizon of such anaxially symmetric black hole (rotating or static) that the metric coefficient$g_{\phi \phi }\rightarrow 0$ there. It is shown that (both for regular andsingular horizons) the energy in the centre of mass frame $% E_{c.m.}$ isindefinitely large even without fine-tuning of particles' parameters.Kinematically, this is collision between two rapid particles that approach thehorizon almost with the speed of light but at different angles. The latter isthe reason why the relative velocity tends to that of light, hence to high$E_{c.m.}$. Our approach is model-independent. It relies on general propertiesof geometry and is insensitive to the details of material source that supportsthe geometies of the type under consideration. For several particular models(the stringy black hole, the Brans-Dicke analogue of the Schwarzschild metricand the Janis-Newman-Winicour one) we recover the results found in literaturepreviously.

High energy particle collisions and geometry of horizon