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

TL;DR

The paper shows that the low-energy response of extremal and near-extremal black holes is governed by near-horizon AdS_2 dynamics, encapsulated by the Schwarzian time-reparametrisation mode and a gauge-field phase mode. By including charged matter, gauge fields, and KK reductions, it derives two- and four-point functions in the AdS_2 throat and demonstrates how these modes reproduce the leading low-energy behavior, with higher partial waves contributing at higher energies. The authors formulate a general near-AdS_2 to NCFT_1 correspondence applicable to AdS_2 x S^d geometries and extend the analysis to asymptotically flat cases, establishing a unifying framework for low-energy black hole dynamics. The work provides a calculational program to capture IR physics of extremal black holes via time reparametrisation and phase modes, potentially connecting to SYK-like dynamics and JT gravity. It also highlights how attractor physics fixes extremal entropy while departures from AdS_2 depend on asymptotic moduli, shaping the IR effective action.

Abstract

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 $AdS_2 \times S^d$ near-horizon geometry arises, including black holes in asymptotically $AdS$ and flat space-times.