Classical gravitational scattering in the relativistic Kepler problem

TL;DR

This paper analyzes the dynamics of hyperbolic orbits around Kerr black holes, deriving scattering and capture cross sections, and extends the study to two-body encounters including gravitational radiation effects.

Contribution

It provides new analytical results for scattering and capture in Kerr spacetime and generalizes to two-body hyperbolic encounters with gravitational radiation effects.

Findings

Derived differential scattering cross section and capture cross section.

Extended analysis to two-body hyperbolic encounters with gravitational radiation.

Explored effects of black hole spin and energy parameters on scattering outcomes.

Abstract

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.