No static bubbling spacetimes in higher dimensional Einstein-Maxwell theory

TL;DR

This paper proves that in higher-dimensional Einstein-Maxwell theory, static asymptotically flat spacetimes cannot have magnetic fields, leading to a complete classification of static black holes and ruling out non-trivial topologies.

Contribution

It establishes the non-existence of static magnetic solutions and static solitons in higher-dimensional Einstein-Maxwell theory, completing the classification of static black holes.

Findings

No static magnetic or soliton solutions exist in the theory.

Static non-extremal black holes are fully classified.

Asymptotically flat static spacetimes with non-trivial topology are absent.

Abstract

We prove that any asymptotically flat static spacetime in higher dimensional Einstein-Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black holes in this theory. In particular, these results establish that there are no asymptotically flat static spacetimes with non-trivial topology, with or without a black hole, in Einstein-Maxwell theory.