Black Holes in Higher-Dimensional Gravity

Abstract

These lectures review some of the recent progress in uncovering the phase structure of black hole solutions in higher-dimensional vacuum Einstein gravity. The two classes on which we focus are Kaluza-Klein black holes, i.e. static solutions with an event horizon in asymptotically flat spaces with compact directions, and stationary solutions with an event horizon in asymptotically flat space. Highlights include the recently constructed multi-black hole configurations on the cylinder and thin rotating black rings in dimensions higher than five. The phase diagram that is emerging for each of the two classes will be discussed, including an intriguing connection that relates the phase structure of Kaluza-Klein black holes with that of asymptotically flat rotating black holes.

latex, 49 pages, 5 figures. Lectures to appear in the proceedings of the Fourth Aegean Summer School, Mytiline, Lesvos, Greece, September 17-22, 2007

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• Black Holes as Lumps of Fluid
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• Rod-structure classification of gravitational instantons with U(1)xU(1) isometry
• Blackfolds in (Anti)-de Sitter Backgrounds
• Interpreting spacetimes of any dimension using geodesic deviation
• Static and rotating black strings in dynamical Chern-Simons modified gravity
• Quasilocal formalism and thermodynamics of asymptotically flat black objects
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• Quasilocal equilibrium condition for black ring
• $d\ge 5$ static black holes with $S^2\times S^{d-4}$ event horizon topology
• The Hawking cascades of gravitons from higher-dimensional Schwarzschild black holes
• Harrison transformation and charged black objects in Kaluza-Klein theory
• Homogeneous Black Strings in Einstein-Gauss-Bonnet with Horndeski hair and beyond
• Einstein-Gauss-Bonnet black strings
• Charged-Rotating Black Holes in Higher-dimensional (A)DS-Gravity
• Caged black hole thermodynamics: Charge, the extremal limit, and finite size effects
• Three types of superpotentials for perturbations in the Einstein-Gauss-Bonnet gravity
• Stabilizing Homogeneous Black Strings in AdS
• Particle Dynamics Around the Black String
• A Toy Model for Topology Change Transitions: Role of Curvature Corrections
• Perturbations of Gauss-Bonnet Black Strings in Codimension-2 Braneworlds
• Charged squashed black holes with negative cosmological constant in odd dimensions
• Static charged double-black rings in five dimensions
• Charged black holes on the Taub-Bolt instanton
• Black stars induced by matter on a brane: exact solutions
• On Universality of Ergoregion Mergers
• First Law of p-brane Thermodynamics
• A black ring on the Taub-bolt instanton in five dimensions
• Stability of the warped black string with nontrivial topology in five-dimensional Anti-de Sitter spacetime
• The Gregory-Laflamme instability and non-uniform generalizations of NUT strings
• Non-extremal near-horizon geometries
• On double-black hole solutions of the Einstein-Maxwell-Dilaton theory in five dimensions
• C-metric like vacuum with non-negative cosmological constant in five dimensions
• String/$\mathcal{M}$-theory Dual of Large-$N$ Thermal QCD-Like Theories at Intermediate Gauge/'t Hooft Coupling and Holographic Phenomenology