Extremal and near-extremal black holes and near-CFT1

We study the behaviour of extremal and near-extremal black holes at low energies and low temperatures and find that it can be understood from the near-horizon AdS(2) region. Our analysis includes charged matter and also goes beyond the S-wave approximation. We find that the leading behaviour at low energies arises from a mode linked to time reparametrisations and from phase modes arising from gauge fields. At somewhat higher energies, additional modes arising from higher partial waves can also be cumulatively significant. These results can be applied quite generally to cases where an AdS(2) x S-d near-horizon geometry arises, including black holes in asymptotically AdS and flat space-times.