Banados-Silk-West effect with nongeodesic particles: Nonextremal   horizons
  When two particles collide near a black hole, the energy in their center of mass frame can, under certain conditions, grow unbounded. This is the Banados-Silk-West effect. We show that this effect retains its validity even if some force acts on a particle, provided some reasonable and weak restrictions are imposed on this force. In the present work we discuss the case of nonextremal horizons. The result under discussion is similar to that for extremal horizons considered in our previous work. 
I.V. Tanatarov and O.B. Zaslavskii
gr-qc astro-ph.HE hep-th