Matter-coupled supersymmetric Kerr-Newman-AdS$_4$ black holes

TL;DR

This work constructs new analytic rotating AdS$_4$ black holes in gauged ${\cal N}=2$ supergravity with vector multiplets and symmetric scalar manifolds, preserving two real supercharges and admitting a smooth BPS limit to Kerr-Newman-AdS$_4$. Using the real, quartic-invariant formulation, the authors derive a general entropy function and solve the BPS equations in a Kerr-Newman-type base, enabling explicit STU-model solutions and an uplift to M-theory on S$^7$. The near-horizon and full-flow analyses yield compact-horizon solutions with computable charges, entropy, and angular momentum, satisfying a BPS mass bound and a horizon-product relation. They provide concrete STU realizations, including the T$^3$ electric truncation and the X$^0$X$^1$ dyonic model, with exact expressions for charges, entropy, and angular momentum, validating the entropy function and linking to holography via the generalized superconformal index.

Abstract

We present new analytic rotating AdS$_4$ black holes, found as solutions of 4d gauged $\mathcal{N}=2$ supergravity coupled to abelian vector multiplets with a symmetric scalar manifold. These configurations preserve two real supercharges and have a smooth limit to the BPS Kerr-Newman-AdS$_4$ black hole. We spell out the solution of the $STU$ model admitting an uplift to M-theory on S$^7$. We identify an entropy function, which upon extremization gives the black hole entropy, to be holographically reproduced by the leading $N$ contribution of the generalized superconformal index of the dual theory.