Stationary Einstein-Maxwell fields in arbitrary dimensions

Abstract

The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic map coupled to gravity on three-dimensional base space generalizing the Ernst system in the four-dimensional stationary Einstein-Maxwell theory. Some classes of the new exact solutions have been provided, which include the electro-magnetic generalization of the Myers-Perry solution, which describes the rotating black hole immersed in a magnetic universe, and the static charged black ring solution.

26 pages

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Cited by in corpus (34)

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• Rotating Circular Strings, and Infinite Non-Uniqueness of Black Rings
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• Algebraic classification of higher dimensional spacetimes based on null alignment
• New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness
• A boundary value problem for the five-dimensional stationary rotating black holes
• Type D Einstein spacetimes in higher dimensions
• Charging axisymmetric space-times with cosmological constant
• Ricci flat rotating black branes with a conformally invariant Maxwell source
• Electrically charged dilatonic black rings
• Higher dimensional black holes in external magnetic fields
• Embedding hairy black holes in a magnetic universe
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• Dilaton black holes with squashed horizons and their thermodynamics
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• On squashed black holes in Godel universes
• Solitonic generation of vacuum solutions in five-dimensional General Relativity
• Magnetic black holes with higher-order curvature and gauge corrections in even dimensions
• Generating technique for $U(1{)}^{3}5D$ supergravity
• Black rings with a small electric charge: gyromagnetic ratios and algebraic alignment
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• Charged Kaluza-Klein double-black holes in five dimensions
• Charged Balanced Black Rings in Five Dimensions
• Rotating dyonic dipole black rings: exact solutions and thermodynamics
• Generalizations and challenges for the spacetime block-diagonalization
• Ultrarelativistic boost of spinning and charged black rings
• Static charged double-black rings in five dimensions
• Bertotti-Robinson solutions of D=5 Einstein-Maxwell-Chern-Simons-Lambda theory
• A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes
• Five-dimensional electrostatic black holes in a background field
• Global properties of higher-dimensional cosmological spacetimes
• Minimal data at a given point of space for solutions to certain geometric systems