On-shell amplitude approach to spinning binaries in GR and beyond

We summarize recent work applying on-shell amplitude techniques to compute classical observables in scalar-tensor theories of gravity. We study gravitational and scalar radiation from spinning compact objects in two scenarios: theories without scalar hair where radiation is generated via curvature couplings of the scalar with the Gauss-Bonnet and Chern-Simons invariants, and theories with scalar hair where a direct conformal coupling leads to prolific dipole emission. Using the Kosower-Maybee-O'Connell (KMOC) formalism, we directly compute waveforms at leading order in the Post-Minkowskian (PM) expansion and the associated memory effects and radiated power. We examine their velocity scaling in the Post-Newtonian (PN) limit and comment on their phenomenological relevance. Throughout we use the spinor-helicity formalism and the unitary factorization techniques to derive the necessary on-shell amplitudes, efficiently computing observables to all orders in spin and velocity, offering powerful tools for gravitational-wave astronomy.