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We study the behaviour of extremal and near-extremal black holes at lowenergies and low temperatures and find that it can be understood from thenear-horizon $AdS_2$ region. Our analysis includes charged matter and also goesbeyond the $S$-wave approximation. We find that the leading behaviour at lowenergies arises from a mode linked to time reparametrisations and from phasemodes arising from gauge fields. At somewhat higher energies, additional modesarising from higher partial waves can also be cumulatively significant. Theseresults can be applied quite generally to cases where an $AdS_2 \times S^d$near-horizon geometry arises, including black holes in asymptotically $AdS$ andflat space-times.

Extremal and Near-Extremal Black Holes and Near-$CFT_1$