The relativistic two-body problem is notoriously hard to solve. It’s non-linearity has long prevented analytical closed form solutions. However, performing weak field expansions, e.g., perturbing around the Newtonian or Minkowskian limit, often simplifies the problem enough to obtain analytic results. At UCD we focus on combinging these weak-field approaches with an expansion in the small mass-ratio to allow for analytical self-force results. This not only bypasses major numerical boundaries, but also allows for clearer and more direct comparisons.
From the point of view of binary scattering, the forefront of modern weak-field expansions use methods from quantum field theory to build relativistic corrections to motion around Minkowski spacetime. At UCD we are investigating how black hole perturbation theory can interface with these approaches.