Supersymmetric $AdS_6$ black holes from matter coupled $F(4)$ gauged supergravity

TL;DR

This paper constructs new supersymmetric $AdS_6$ black hole solutions with various horizon geometries in matter coupled $F(4)$ gauged supergravity, including numerical solutions and interpolating geometries.

Contribution

It introduces novel supersymmetric $AdS_6$ black hole solutions with complex horizon topologies, expanding understanding of supergravity black holes in six dimensions.

Findings

New $AdS_2 imes ext{Riemann surfaces}$ horizons with higher genus

Numerical black hole solutions interpolating between $AdS_6$ and $AdS_2$ horizons

Black holes with Kähler and Cayley four-cycle horizons in special manifolds

Abstract

In matter coupled $F(4)$ gauged supergravity in six dimensions, we study supersymmetric $AdS_6$ black holes with various horizon geometries. We find new $AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizons with $\mathfrak{g}_1>1$ and $\mathfrak{g}_2>1$, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically $AdS_6$ boundary and the $AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizon. We also find black holes with horizons of K\"ahler four-cycles in Calabi-Yau fourfolds and Cayley four-cycles in $Spin(7)$ manifolds.