# General Supersymmetric AdS$_5$ Black Holes with Squashed Boundary

## TL;DR

This paper introduces a new family of supersymmetric AdS$_5$ black hole solutions with squashed boundaries, characterized by three parameters, and explores their physical properties and thermodynamics using holographic methods.

## Contribution

It presents novel asymptotically locally AdS$_5$ supersymmetric black holes with squashed boundaries, including their uplift to type IIB supergravity and analysis of their charges.

## Key findings

- Entropy is independent of squashing.
- Page charges differ from holographic charges due to Chern-Simons term.
- Thermodynamics is better described by Page charges.

## Abstract

We present a new family of asymptotically locally AdS$_5$ squashed supersymmetric black hole solutions of Fayet-Iliopoulos gauged ${\cal N}=2$, $D=5$ supergravity with two vector multiplets that have a natural uplift to type IIB supergravity. Our new family of black holes is characterized by three parameters, of which two control the horizon geometry while the latter regulates the squashing at the boundary. We evaluate the main physical properties of the family of solutions using holographic renormalization and find that the entropy is independent on the squashing and it is reproduced by using the angular momentum and the Page charges. In previously known solutions Page and holographic charges are equal, due to the vanishing of the Chern-Simons term that here, instead, is relevant. This result suggests that for asymptotically locally AdS$_5$ solutions we should refer to the Page charges to describe the thermodynamics of the system.