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

TL;DR

This paper constructs higher-dimensional static black hole solutions with specific horizon topologies, analyzing their properties and how external magnetic fields can balance them in asymptotically flat spacetimes.

Contribution

It introduces new static, nonextremal black hole solutions in 6 and 7 dimensions with $S^2\times S^{d-4}$ horizons and explores their behavior under external magnetic fields.

Findings

Solutions exist in 6 and 7 dimensions with specified horizon topology.

Balanced configurations can be achieved with a critical external magnetic field.

Solutions approach a Melvin universe background asymptotically.

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.