Behind every numerical waveform lies an analytical scaffolding. The two-timescale expansion that organises the EMRI problem — separating fast orbital motion from slow inspiral evolution — must be developed systematically order by order in the mass ratio. This analytical work establishes what quantities are needed at each order, how they can be computed, and what cross-checks are available to validate the numerical results.
Our analytical work spans the multiscale expansion of the Einstein field equations, post-Newtonian and post-Minkowskian techniques in regimes accessible to perturbation theory, resummation methods that extend the reach of perturbative results, and exact and approximate solutions in special limits. This analytical foundation guides the numerical work, provides essential cross-checks on computed waveforms, and connects self-force theory to the broader landscape of gravitational two-body dynamics.
Current focus:
- Two-timescale expansion at second post-adiabatic order
- Post-Newtonian self-force calculations and high-order coefficients
- Resonance phenomena and resonance-crossing dynamics
- Exact solutions in special geometries and limits