# Charges from Attractors

## TL;DR

This paper develops a method to extract the quantum numbers of extremal black holes from their near-horizon geometries using gravitational charges, applicable to various supergravity theories and connecting to thermodynamics and entropy formalism.

## Contribution

It introduces a unified approach to recover black hole charges from near-horizon data using Noether-Wald charges, applicable to extremal and non-extremal cases, with explicit derivations in supergravity.

## Key findings

- Successfully derives black hole charges from near-horizon geometries.
- Shows equivalence of gravitational charges to U(1) charges in reduced solutions.
- Connects near-horizon analysis to thermodynamic quantities and entropy formalism.

## Abstract

We describe how to recover the quantum numbers of extremal black holes from their near horizon geometries. This is achieved by constructing the gravitational Noether-Wald charges which can be used for non-extremal black holes as well. These charges are shown to be equivalent to the U(1) charges of appropriately dimensionally reduced solutions. Explicit derivations are provided for 10 dimensional type IIB supergravity and 5 dimensional minimal gauged supergravity, with illustrative examples for various black hole solutions. We also discuss how to derive the thermodynamic quantities and their relations explicitly in the extremal limit, from the point of view of the near-horizon geometry. We relate our results to the entropy function formalism.