# The Scales of Black Holes with nAdS$_2$ Geometry

## TL;DR

This paper investigates the scales of nearly AdS$_2$ regions in nearly extremal black holes across various string-inspired settings, linking these scales to microscopic theories and the attractor mechanism.

## Contribution

It generalizes the attractor mechanism to determine the scales of nAdS$_2$ regions and explores their geometric and charge-dependent properties in diverse black hole solutions.

## Key findings

- Scales are determined by a generalized attractor mechanism.
- Geometric realization via normal derivatives along attractor flow.
- Charge dependence of extremal attractor influences the scales.

## 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.