Rotating black holes with Nil or SL(2,$\,\mathbb{R}$) horizons

TL;DR

This paper constructs and analyzes new rotating black hole solutions in five-dimensional supergravity with Nil and SL(2,R) horizon geometries, revealing novel supersymmetric and nonextremal properties and their dimensional reductions.

Contribution

It introduces the first SL(2,R) horizon black hole in supergravity and provides new solutions with Nil horizons, expanding the landscape of known black hole geometries.

Findings

Constructed a rotating SL(2,R) horizon black hole with supersymmetry.

Derived a nonextremal Nil black hole from Kerr-AdS$_5$ via scaling.

Obtained a new charged hyperbolic horizon solution in 4D.

Abstract

We construct rotating black holes in $N=2$, $D=5$ minimal and matter-coupled gauged supergravity, with horizons that are homogeneous but not isotropic. Such spaces belong to the eight Thurston model geometries, out of which we consider the cases Nil and SL$(2,\mathbb{R})$. In the former, we use the recipe of arXiv:hep-th/0304064 to directly rederive the solution that was obtained by Gutowski and Reall in arXiv:hep-th/0401042 as a scaling limit from a spherical black hole. With the same techniques, the first example of a black hole with SL$(2,\mathbb{R})$ horizon is constructed, which is rotating and one quarter BPS. The physical properties of this solution are discussed, and it is shown that in the near-horizon limit it boils down to the geometry of arXiv:hep-th/0401042, with a supersymmetry enhancement to one half. Dimensional reduction to $D=4$ gives a new solution with hyperbolic horizon to the t$^3$ model that carries both electric and magnetic charges. Moreover, we show how to get a nonextremal rotating Nil black hole by applying a certain scaling limit to Kerr-AdS$_5$ with two equal rotation parameters, which consists in zooming onto the north pole of the S$^2$ over which the S$^3$ is fibered, while boosting the horizon velocity effectively to the speed of light.