The Scales of Black Holes with nAdS$_2$ Geometry

TL;DR

The paper develops a general nAttractor framework connecting the IR scale of near-AdS$_2$ horizons to UV data via extremal attractor flows and extends it to near-extremal black holes (nAdS$_2$). It presents a standard radial-derivative formulation and a stronger charge-space gradient version, providing explicit length-scale formulas for entropy and horizon scalars in higher dimensions, AdS$_4$, and rotating black holes, with detailed 5D STU model examples. It shows that near-extremal thermodynamics can be computed from extremal data, but that the strong nAttractor mechanism is model-dependent and requires special structures (e.g., linear harmonic functions) to hold generally. The results illuminate the UV/IR interplay in nearly AdS$_2$ holography and offer practical tools for quantifying IR physics from UV charges and asymptotic moduli.

Abstract

We study nearly extreme black holes with nearly AdS$_2$ horizon geometry in various settings inspired by string theory. Our focus is on the scales of the nAdS$_2$ region and their relation to microscopic theory. These scales are determined by a generalization of the attractor mechanism for extremal black holes and realized geometrically as the normal derivatives along the extremal attractor flow. In some cases the scales are equivalently determined by the charge dependence of the extremal attractor by itself. Our examples include near extreme black holes in $D\geq 4$ dimensions, AdS boundary conditions, rotation, and 5D black holes on the non-BPS branch.