AdS$_2$/CFT$_1$ correspondence and near-extremal black hole entropy

TL;DR

This work demonstrates that the near-horizon AdS$_2$ geometries of near-extremal black holes admit a CFT$_1$ described by their asymptotic Virasoro symmetry, enabling Cardy’s formula to account not only for the extremal BTZ and Reissner–Nordström entropies but also for the leading deviation from extremality. Through dimensional reduction to a two-dimensional dilaton gravity (including Jackiw–Teitelboim theory in the spinless sector), the authors compute the central charge and L0 from boundary charges and show that the resulting microscopic entropy changes exactly reproduce the thermodynamic near-extremal entropy, $S_e + \Delta S$, for near-extremal BTZ, RN, and a broad class of black holes. They further generalize the construction to arbitrary black holes described by 2D dilaton gravity, establishing a universal link between near-extremal entropy and AdS$_2$/CFT$_1$ holography. The results underscore the universality of holographic entropy counting in near-extremal regimes and clarify the role of AdS$_2$ boundary symmetries in black hole thermodynamics.

Abstract

We provide a realization of the AdS$_2$/CFT$_1$ correspondence in terms of asymptotic symmetries of the AdS$_2\times$S$^1$ and AdS$_2\times$S$^2$ geometries arising in near-extremal BTZ and Reissner-Nordström black holes. Cardy's formula exactly accounts for the deviation of the Bekenstein-Hawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality.