Extreme Mass Ratio Inspirals with Scalar Hair

Stellar mass objects orbiting around supermassive black holes are primary targets for future gravitational wave detectors like LISA. However, in theories beyond general relativity, the corresponding waveform templates are still relatively poorly known. We propose a universal description for these systems which applies to any black hole with a non trivial scalar profile, or scalar hair. To this aim, we use the effective field theory recently introduced by Franciolini et al. to write the most general action for the perturbations of a spherically symmetric solution up to some given order in derivatives and/or number of fields. At any post-Newtonian order, the background metric and the relevant operators can be encoded in a limited number of parameters which are readily calculated in some given scalar tensor model, as we show with a couple of examples. In terms of such parameters, we obtain an analytic expression for the dissipated power in the odd sector by solving perturbatively the Regge-Wheeler equation in the presence of a point-particle source.