$d\geq 5$ magnetized static, balanced black holes with $S^2\times S^{d-4}$ event horizon topology

Abstract

We construct static, nonextremal black hole solutions of the Einstein-Maxwell equations in $d=6,7$ spacetime dimensions, with an event horizon of $S^2\times S^{d-4}$ topology. These configurations are asymptotically flat, the U(1) field being purely magnetic, with a spherical distribution of monopole charges but no net charge measured at infinity. They can be viewed as generalizations of the $d=5$ static dipole black ring, sharing its basic properties, in particular the presence of a conical singularity. The magnetized version of these solutions is constructed by applying a Harrison transformation, which puts them into an external magnetic field. For $d=5,6,7$, balanced configurations approaching asymptotically a Melvin universe background are found for a critical value of the background magnetic field.