Horizon instability of the extremal BTZ black hole

Extremal black holes exhibit a universal horizon instability (Aretakis instability). We study the simplest possible system, a scalar field perturbing the BTZ black hole, and obtain the retarded Green function in closed form, allowing us to unite different methods used previously for special cases. We hope this insight will be useful in unravelling the astrophysical and holographic implications of this universal instability.