A uniqueness theorem for stationary Kaluza-Klein black holes

Abstract

We prove a uniqueness theorem for stationary $D$-dimensional Kaluza-Klein black holes with $D-2$ Killing fields, generating the symmetry group $\mathbb{R}\times U(1{)}^{D-3}$. It is shown that the topology and metric of such black holes is uniquely determined by the angular momenta and certain other invariants consisting of a number of real moduli, as well as integer vectors subject to certain constraints.

Latex, 38 pages, no figures; v2: removed condition from statement of main theorem, additional material on spacetime topology, references added

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• New black holes of vacuum Einstein equations with hyperscaling violation and Nil geometry horizons
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• New Restrictions on the Topology of Extreme Black Holes
• Existence and uniqueness of asymptotically flat toric gravitational instantons
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• Toric gravitational instantons in gauged supergravity
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• Black hole uniqueness theorems and new thermodynamic identities in eleven dimensional supergravity
• New thermodynamic identities for five-dimensional black holes
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• Soliton mechanics
• Balancing Static Vacuum Black Holes with Signed Masses in 4 and 5 Dimensions
• 5-Dimensional Space-Periodic Solutions of the Static Vacuum Einstein Equations
• Charged black holes on the Taub-Bolt instanton
• Domain Structure of Black Hole Space-Times with a Cosmological Constant
• Uniqueness of Black Holes with Bubbles in Minimal Supergravity
• A black ring on the Taub-bolt instanton in five dimensions
• Integrability in Gravity from Chern-Simons Theory
• The Angular Tension of Black Holes
• A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry
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• Kaluza-Klein rotating multi-black hole configurations with electromagnetic field in Einstein-Maxwell-dilaton gravity
• N=4 Near-Horizon Geometries in D=11 Supergravity