Inspirals into Gargantua

We model the inspiral of a compact, stellar mass object into a massive black hole rotating at or just below the theoretical maximum. We find that once the compact object enters the near-horizon regime the gravitational radiation is characterized by a constant frequency, equal to the horizon frequency, with an exponentially damped profile. This contrasts with the usual `chirping' behaviour of a black hole binary system and were such a waveform observed it would constitute a `smoking gun' for a (near) extremal black hole in nature.