# AdS$_5$ Black Hole Entropy near the BPS Limit

## TL;DR

This paper investigates the thermodynamics and microscopic entropy calculations of AdS$_5$ black holes close to the BPS limit, revealing how near-extremal deviations affect entropy and match microscopic predictions.

## Contribution

It extends microscopic entropy computations from BPS to nearBPS black holes by relaxing supersymmetry constraints, aligning microscopic and gravitational results.

## Key findings

- Microscopic entropy matches gravitational calculations for nearBPS black holes.
- Deviations from BPS conditions are characterized by temperature and potential constraints.
- The study generalizes methods to analyze near-extremal black hole thermodynamics.

## Abstract

We analyze AdS$_5$ black holes that are nearly supersymmetric. They depart from the BPS limit in two distinct ways: a temperature takes them above extremality and a potential violates a certain constraint. We study the thermodynamics of these deformations and their interplay in detail. We discuss recent microscopic computations of BPS black hole entropy in $\mathcal{N}=4$ SYM and generalize methods to the nearBPS regime by relaxing constraints imposed by supersymmetry. The computations recover gravitational results from microscopics also for nearBPS black holes.