All Vacuum Near-Horizon Geometries in $D$-dimensions with $(D-3)$ Commuting Rotational Symmetries

Abstract

We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2\times T^{D-4}$, or $S^3\times T^{D-5}$, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as $(D-2)(D-3)/2$ continuous parameters. Not all of our metrics in $D\ge 6$ seem to arise as the near horizon limits of known black hole solutions.

22 pages, Latex, no figures, title changed, references added, discussion of the parameters specifying solutions corrected, amended to match published version

References in corpus (12)

• Near-horizon symmetries of extremal black holes
• CFT Duals for Extreme Black Holes
• Kerr-AdS/CFT Correspondence in Diverse Dimensions
• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• No Dynamics in the Extremal Kerr Throat
• A classification of near-horizon geometries of extremal vacuum black holes
• Central Charges in Extreme Black Hole/CFT Correspondence
• Extremal vacuum black holes in higher dimensions
• The Kerr/CFT Correspondence and String Theory
• Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes
• Uniqueness of Extremal Kerr and Kerr-Newman Black Holes
• On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

Cited by in corpus (34)

• Stationary Black Holes: Uniqueness and Beyond
• Classification of near-horizon geometries of extremal black holes
• Black hole uniqueness theorems in higher dimensional spacetimes
• NR/HEP: roadmap for the future
• Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
• Wiggling Throat of Extremal Black Holes
• Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra
• Horizon hair of extremal black holes and measurements at null infinity
• An infinite class of extremal horizons in higher dimensions
• Conserved charges, surface degrees of freedom, and black hole entropy
• Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics
• Horizon area-angular momentum inequality in higher dimensional spacetimes
• On Thermodynamics and Phase Space of Near Horizon Extremal Geometries
• Emergent AdS_3 in the Zero Entropy Extremal Black Holes
• Near Horizon Structure of Extremal Vanishing Horizon Black Holes
• Towards uniqueness of degenerate axially symmetric Killing horizon
• Three Theorems on Near Horizon Extremal Vanishing Horizon Geometries
• Constructing near-horizon geometries in supergravities with hidden symmetry
• Extremal Sasakian horizons
• Extremal Vanishing Horizon Kerr-AdS Black Holes at Ultraspinning Limit
• Conformal weights in the Kerr/CFT correspondence
• Massive vector field perturbations on extremal and near-extremal static black holes
• AdS${}_3$ to dS${}_3$ transition in the near horizon of asymptotically de Sitter solutions
• Massive tensor field perturbations on extremal and near-extremal static black holes
• Some spacetimes containing non-rotating extremal isolated horizons
• Electrovacuum Near-horizon Geometries in Four and Five Dimensions
• Mathematical general relativity: a sampler
• Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity
• On the nonexistence of extreme anti-de Sitter black rings
• Instability in near-horizon geometries of even-dimensional Myers-Perry black holes
• Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes
• Degenerate horizons, Einstein metrics, and Lens space bundles
• Non-existence of toroidal cohomogeneity-1 near horizon geometries
• Near-Horizon Extremal Geometries: Coadjoint Orbits and Quantization