# An extremization principle for the entropy of rotating BPS black holes in AdS$_5$

## TL;DR

The paper introduces an extremization principle that reproduces the entropy of certain BPS rotating black holes in AdS$_5$, potentially linked to the attractor mechanism in five-dimensional gauged supergravity.

## Contribution

It proposes a novel extremization approach to compute black hole entropy, connecting it to anomaly polynomials and supersymmetric Casimir energy in $ ext{AdS}_5$/CFT$_4$ correspondence.

## Key findings

- Entropy obtained via extremization matches Bekenstein-Hawking entropy.
- The extremization expression resembles anomaly polynomials and Casimir energy.
- Suggests a link to the attractor mechanism in gauged supergravity.

## Abstract

We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS$_5\times S^5$ can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for $\mathcal{N}=4$ super Yang-Mills.