Analytic Properties of High Spin & Large Mass-ratio Coalescences

I will review the derivation of gravitational waveforms for binaries with large mass ratios based on conformal symmetry methods. I will first motivate the astrophysics of intermediate mass ratio inspirals and black holes with very high spin. I will then turn to review the near-horizon properties of the high spin Kerr black hole and I will outline the conformal symmetry methods to derive gravitational waveforms. I will derive the key signatures of such waveforms. I will end by extending the point particle limit to finite size corrections using the Mathisson-Papapetrou-Dixon formalism.