On the smoothness of static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory

Abstract

Previous work has shown that static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory do not possess smooth horizons. We show that the lack of smoothness is worse than previously demonstrated. We consider solutions describing multiple black holes on a common axis. In five dimensions, the metric is generically twice, but not three times, continuously differentiable at the horizon. The Maxwell field is generically continuous, but not differentiable, at the horizon. In more than five dimensions, the metric is once, but not twice, continuously differentiable, and there is a parallely-propagated curvature singularity at the horizon. The Maxwell field strength is again continuous, but not differentiable, at the horizon.

arXiv comment19 pages; minor corrections

References in corpus (5)

• Higher-dimensional resolution of dilatonic black hole singularities
• On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• Supersymmetric Self-Gravitating Solitons
• Testing Cosmic Censorship with Black Hole Collisions
• On the Smoothness of the Horizons of Multi-Black Hole Solutions

Cited by in corpus (28)

• Black Holes in Higher Dimensions
• Classification of near-horizon geometries of extremal black holes
• On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
• Almost all extremal black holes in AdS are singular
• Interpreting spacetimes of any dimension using geodesic deviation
• Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
• Cosmological Solutions on Atiyah-Hitchin Space in Five Dimensional Einstein-Maxwell-Chern-Simons Theory
• All higher-dimensional Majumdar-Papapetrou black holes
• Extremal Charged Black Holes with a Twisted Extra Dimension
• Stable circular orbits in higher-dimensional multi-black hole spacetimes
• Uniqueness of the extremal Schwarzschild de Sitter spacetime
• Cosmological Solutions in Five Dimensional Minimal Supergravity
• Analyticity of Event Horizons of Five-Dimensional Multi-Black Holes with Non-Trivial Asymptotic Structure
• Supersymmetric black holes with a single axial symmetry in five dimensions
• A simple diagnosis of non-smoothness of black hole horizon: Curvature singularity at horizons in extremal Kaluza-Klein black holes
• Asymptotically flat multi-black lenses
• On the smoothness of the multi-BMPV black hole spacetime
• Existence and absence of Killing horizons in static solutions with symmetries
• Higher-dimensional Buchdahl and Janis-Robinson-Winicour transformations in the Einstein-Maxwell system with a massless scalar field
• A pair of extremal charged black holes on Kerr-Taub-bolt space
• Force-free higher derivative Einstein-Maxwell theory and multi-centered black holes
• Charged black strings in a five-dimensional Kasner universe
• Dynamical Black Rings with a Positive Cosmological Constant
• Vacuum-dual static perfect fluid obeying $p=-(n-3)\rho /(n+1)$ in $n(\ge 4)$ dimensions
• Topology Changing Process of Coalescing Black Holes on Eguchi-Hanson Space
• On the smoothness of multi-M2 brane horizons
• EFT Corrections to Majumdar-Papapetrou Black Holes
• Remarks on nonperturbative perturbations