Kinematics of Two-particle Scattering in Black Hole Backgrounds

We show that particle scattering in general curved backgrounds entails {\it six} independent, kinematical Mandelstam-like invariants, instead of the two in flat spacetime. Spacetime isometries are shown to lead to constraints between these parameters, so that for standard black holes like Schwarzschild, Reissner-Nordstr\"om, or Kerr spacetimes, the number of {\it independent} parameters may be less than six. We compute the values of these independent parameters very close to the event horizon of the black holes. We demonstrate the existence of kinematical domains in the parameter space of particle trajectories for which some of the independent invariants may become unbounded above, as the point of collision approaches the event horizon. For particle scattering, this would imply the possibility of scattering with very large center-of-mass energy squared and/or very large momentum-transferred squared, making this astrophysically a laboratory for physics beyond the standard model.
Comment: 7 pages