No static bubbling spacetimes in higher dimensional Einstein-Maxwell theory

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.

9 pages. v2: minor edits, references added

References in corpus (5)

• Instability of supersymmetric microstate geometries
• Classification of Static Charged Black Holes in Higher Dimensions
• On higher dimensional black holes with abelian isometry group
• No-dipole-hair theorem for higher-dimensional static black holes
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• Uniqueness of the extremal Schwarzschild de Sitter spacetime
• Divergence equations and uniqueness theorem of static black holes
• On the geometry of electrovacuum spaces in higher dimensions
• Lower bound for angular momenta of microstate geometries in five dimensions
• Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
• Five-dimensional electrostatic black holes in a background field
• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
• Mean-stable surfaces in Static Einstein-Maxwell theory
• A Penrose-type inequality for static spacetimes
• Supersymmetric multi-charge solitons in AdS${}_5$