# Kinematics of Two-particle Scattering in Black Hole Backgrounds

## TL;DR

This paper investigates the kinematics of two-particle scattering near black holes, revealing six invariants in curved spacetime and their potential to become unbounded near horizons, suggesting possible high-energy phenomena.

## Contribution

It introduces a framework for analyzing particle scattering in curved backgrounds with six invariants and explores their behavior near black hole horizons, highlighting new high-energy scattering possibilities.

## Key findings

- Six independent kinematic invariants in curved spacetime.
- Constraints reduce invariants for standard black holes.
- Unbounded invariants near the event horizon.

## Abstract

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.