Probing time-dependent scalar wigs with extreme-mass-ratio inspirals

We investigate the gravitational wave emission from extreme mass ratio inspirals, key targets for the upcoming space-based detector LISA, considering the scenario where the lighter black hole in the binary is endowed by a long-lived, time-dependent scalar field configuration, known as a scalar wig. We develop a formalism to compute scalar perturbations for extreme mass ratio inspirals on circular orbits around Schwarzschild and Kerr black holes, and apply this framework to compute additional fluxes induced by the scalar wig as well as their dependence on the scalar field properties. Our computation provides strong indications that in this scenario the presence of the scalar field does not significantly affect the orbital motion and the gravitational waveform.