On the Structure of Stationary and Axisymmetric Metrics

Abstract

We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of General Relativity in four and higher dimensions, building on recent work in hep-th/0408141. We write the Einstein equations in a new form that naturally identifies the sources for such metrics. The sources live in a one-dimensional subspace and the entire metric is uniquely determined by them. We study in detail the structure of stationary and axisymmetric metrics in four dimensions, and consider as an example the sources of the Kerr black hole.

22 pages. v2: Presentation improved, ref. added

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• Uniqueness theorem for charged rotating black holes in five-dimensional minimal supergravity
• Black Holes in Higher-Dimensional Gravity
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• A uniqueness theorem for stationary Kaluza-Klein black holes
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• Rotating spacetimes with a cosmological constant
• Uniqueness theorem for charged dipole rings in five-dimensional minimal supergravity
• Extremal Black Hole Horizons
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• Domain Structure of Black Hole Space-Times
• Uniqueness Theorem for Black Hole Space-Times with Multiple Disconnected Horizons
• Toric gravitational instantons in gauged supergravity
• Uniqueness theorems for Kaluza-Klein black holes in five-dimensional minimal supergravity
• Doubly Spinning Black Rings
• Rotating spacetimes with a free scalar field in four and five dimensions
• Domain Structure of Black Hole Space-Times with a Cosmological Constant
• Cohomogeneity-1 solutions in Einstein-Maxwell-dilaton gravity
• Uniqueness of Black Holes with Bubbles in Minimal Supergravity
• Mathematical general relativity: a sampler
• First Law of p-brane Thermodynamics
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• Revisiting PBH accretion, evaporation and their cosmological consequences
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• An Elementary Derivation of the Five Dimensional Myers-Perry Metric
• How to Stop (Worrying and Love) the Bubble: Boundary Changing Solutions
• Black hole solutions of modified gravity theories