Near-horizon limit of the charged BTZ black hole and AdS_2 quantum gravity

TL;DR

This paper demonstrates how the charged BTZ black hole connects two distinct AdS_2 geometries, revealing insights into 2D quantum gravity and the role of U(1) charge in the near-horizon and asymptotic regimes.

Contribution

It shows that the charged BTZ black hole interpolates between two different AdS_2 formulations, linking near-horizon and asymptotic geometries in 2D quantum gravity.

Findings

The asymptotic CFT central charge c_as = 3l/G.

The near-horizon CFT central charge c_nh rac{lQ}{\u221a{G}}.

The black hole acts as an interpolator between two AdS_2 descriptions.

Abstract

We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, near-horizon AdS_2 geometry with constant dilaton and U(1) field and an asymptotic AdS_2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS_2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge c_as of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, c_as=3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, c_nh \propto l Q/\sqrt G.