Frequency evolution of gravitational wave signals charaterizing black hole superradiance

An ultralight bosonic field can extract energy from a spinning black hole through superradiance. A boson cloud can thus grow from a single particle in a gravitationally bound state. Once the black hole is maximally spun down, the condition for superradiance is no longer satisfied, and the cloud stops growing. The cloud can then dissipate through gravitational radiation, which in turn may be detected by gravitational wave observations. This suggests it may be possible to use black holes as indirect particle detectors for ultralight bosons (including some dark matter candidates). An accurate waveform model of the gravitational radiation expected would allow us to perform sensitive searches for such new particles. With this end in view, this work outlines a relativistic calculation of the time dependence of the radiation frequency.