Domain Structure of Black Hole Space-Times

Abstract

We introduce the domain structure for stationary black hole space-times. Given a set of commuting Killing vector fields of the space-time the domain structure lives on the submanifold where at least one of the Killing vector fields have zero norm. Depending on which Killing vector field has zero norm the submanifold is naturally divided into domains. A domain corresponds either to a set of fixed points of a spatial symmetry or to a Killing horizon, depending on whether the characterizing Killing vector field is space-like or time-like near the domain. The domain structure provides invariants of the space-time, both topological and geometrical. It is defined for any space-time dimension and any number of commuting Killing vector fields. We examine the domain structure for asymptotically flat space-times and find a canonical form for the metric of such space-times. The domain structure generalizes the rod structure introduced for space-times with D-2 commuting Killing vector fields. We analyze in detail the domain structure for Minkowski space, the Schwarzschild-Tangherlini black hole and the Myers-Perry black hole in six and seven dimensions. Finally we consider the possible domain structures for asymptotically flat black holes in six and seven dimensions.

32 pages, 5 figures. v2: Minor corrections. v3: Language regarding zero norm Killing vector fields made more precise, terminology improved

References in corpus (8)

• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Bicycling Black Rings
• Symmetries of Higher Dimensional Black Holes
• Orthogonal black di-ring solution
• A Uniqueness theorem for 5-dimensional Einstein-Maxwell black holes
• Stationary axisymmetric solutions of five dimensional gravity
• $d\ge 5$ static black holes with $S^2\times S^{d-4}$ event horizon topology

Cited by in corpus (16)

• Numerical Methods for Finding Stationary Gravitational Solutions
• A numerical approach to finding general stationary vacuum black holes
• Black hole uniqueness theorems in higher dimensional spacetimes
• Stationary holographic plasma quenches and numerical methods for non-Killing horizons
• Rod-structure classification of gravitational instantons with U(1)xU(1) isometry
• Blackfolds in (Anti)-de Sitter Backgrounds
• Further restrictions on the topology of stationary black holes in five dimensions
• Uniqueness Theorem for Black Hole Space-Times with Multiple Disconnected Horizons
• A new form of the C-metric with cosmological constant
• Domain Structure of Black Hole Space-Times with a Cosmological Constant
• Uniqueness of Black Holes with Bubbles in Minimal Supergravity
• The Angular Tension of Black Holes
• Remarks on mass and angular momenta for $U(1{)}^2$-invariant initial data
• Charged C-metric in conformal gravity
• Light-ring pairs from $A$-discriminantal varieties
• Second order gauge invariant measure of a tidally deformed black hole