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

TL;DR

This paper analyzes the low-energy behavior of extremal and near-extremal black holes using near-horizon $AdS_2$ geometry, revealing dominant modes from reparametrizations and gauge fields, applicable to various spacetime backgrounds.

Contribution

It extends previous studies by including charged matter and higher partial waves, providing a more comprehensive understanding of black hole near-horizon dynamics.

Findings

Low-energy behavior governed by time reparametrisation modes.

Phase modes from gauge fields are significant.

Higher partial waves contribute at higher energies.

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.