  Black holes are an ubiquitous end state of stellar evolution and successfully
explain some of the most extreme physics encountered in astronomical
observations. The Kerr geometry is the known exact solution to Einstein's
equations for a static, eternal black hole within the framework of general
relativity, and hence is of great importance in relativistic astrophysics. An
understanding of the orbital dynamics of test bodies and light rays in the Kerr
spacetime is therefore fundamental to the physics of a black hole. In this
work, the scattering and capturing properties of unbound, "hyperbolic" orbits
in the spacetime are studied. In particular, the differential scattering cross
section and capture cross section are derived over the parameter space of
energies, impact parameters and black hole spin orientation and magnitude. The
problem is then generalized to the motion of two massive objects on a
hyperbolic encounter, and the added effects of gravitational radiation and
finite mass ratio studied within the post-Newtonian formalism.
