# Rotating black holes in the FI-gauged $N=2$, $D=4$ $\overline{\mathbb{C}\text{P}}^n$ model

## TL;DR

This paper constructs and analyzes supersymmetric rotating black holes in a specific supergravity model, revealing their thermodynamic properties and potential for microscopic entropy calculations.

## Contribution

It provides new explicit solutions for rotating BPS black holes in FI-gauged supergravity, including nonextremal generalizations and thermodynamic relations.

## Key findings

- Constructed supersymmetric rotating black holes with NUT charge.
- Derived a Carter-Plebański-type metric for nonextremal solutions.
- Established thermodynamic laws and a mass formula for these black holes.

## Abstract

We construct supersymmetric black holes with rotation or NUT charge for the $\overline{\mathbb{C}\text{P}}^n$- and the $\text{t}^3$ model of $N=2$, $D=4$ $\text{U}(1)$ FI-gauged supergravity. The solutions preserve 2 real supercharges, which are doubled for their near-horizon geometry. For the $\overline{\mathbb{C}\text{P}}^n$ model we also present a generalization to the nonextremal case, which turns out to be characterized by a Carter-Pleba\'nski-type metric, and has $n+3$ independent parameters, corresponding to mass, angular momentum as well as $n+1$ magnetic charges. We discuss the thermodynamics of these solutions, obtain a Christodoulou-Ruffini mass formula, and shew that they obey a first law of thermodynamics and that the product of horizon areas depends on the angular momentum and the magnetic charges only. At least some of the BPS black holes that we obtain may become instrumental for future microscopic entropy computations involving a supersymmetric index.