Environmental effects in extreme-mass-ratio inspirals: perturbations to the environment in Kerr spacetimes

Future gravitational wave observatories open a unique avenue to study the environments surrounding black holes. Intermediate or extreme mass ratio inspirals will spend thousands to millions of cycles in the sensitivity range of detectors, allowing subtle environmental effects to accumulate in the gravitational waveform. Working in Lorenz gauge and considering equatorial circular orbits, we present the first self-consistent, fully relativistic calculation of a perturbation to a black hole environment due to an inspiraling secondary in the Kerr geometry. As an example case, we consider the environment to be that of a superradiantly grown scalar cloud, though our framework is generalizable to other scenarios. We demonstrate that the scalar field develops a rich wake structure induced by the secondary and compute scalar fluxes emitted to infinity and through the horizon. Relative differences in the fluxes compared to Schwarzschild are tens of percent on large intervals of parameter space, underscoring the importance of modeling in Kerr.