Are Near $AdS_2$ Spacetimes Dual to $AdS_2$ Black Holes?

TL;DR

This paper establishes a one-to-one correspondence between near-AdS2 spacetimes and dilatonic AdS2 black holes, showing they share thermodynamics, can be described by the same 1D CFT states, and are essentially the same solutions under field redefinition.

Contribution

It demonstrates the equivalence of near-AdS2 geometries and dilatonic AdS2 black holes, linking their thermodynamics, boundary deformations, and solution sets through field redefinitions.

Findings

Near-AdS2 spacetimes and dilatonic AdS2 black holes are equivalent.

Both share identical thermodynamic properties.

Boundary deformations match the conformal factor of the black hole metric.

Abstract

We claim that there is a one to one correspondence between $NAdS_2$ spacetimes and dilatonic $AdS_2$ black holes. We show that these have the same thermodynamics and can be described by the same states of 1D CFTs with the same central charge. In addition, we show that these are actually the same set of solutions since a field redefinition in the Schwarzian theory transforms its equation of motion into the time independent part of the bulk Einstein equation. The deformations of the $AdS_2$ boundary as a function of the boundary time are exactly the conformal factor of the $AdS_2$ black hole metric as a function of the radial bulk coordinate.