Hidden Symmetry and Exact Solutions in Einstein Gravity

Abstract

Conformal Killing-Yano tensors are introduced as a generalization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of both hidden symmetries and isometries. We review a classification of higher-dimensional spacetimes admitting such a tensor, and present exact solutions to the Einstein equations for these spacetimes.

Invited review for Prog. Theor. Phys. Suppl, 39 pages, 1 figure, 2 tables

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• Algebraic classification of higher dimensional spacetimes based on null alignment
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• The exact dynamical Chern Simons metric for a spinning black hole possesses a fourth constant of motion: A Dynamical-Systems-Based Conjecture
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
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• A simple test for spacetime symmetry
• Geometry of Lax pairs: particle motion and Killing-Yano tensors
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• Planar solutions of higher-spin theory I: free field level
• General Wahlquist Metrics in All Dimensions
• Rational first integrals of geodesic equations and generalised hidden symmetries
• Prescriptions for measuring and transporting local angular momenta in general relativity
• Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution
• Weakly charged generalized Kerr-NUT-(A)dS spacetimes
• Killing-Yano forms and Killing tensors on a warped space
• On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime
• A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
• Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions
• A Class of Integrable Metrics
• Scale invariance and constants of motion
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• Strong-field gravitational lensing by black holes
• Hidden Symmetries and Integrability in Higher Dimensional Rotating Black Hole Spacetimes
• No more CKY two-forms in the NHEK
• An alternative to the Simon tensor
• Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring
• Degenerate horizons, Einstein metrics, and Lens space bundles
• Higher-dimensional lifts of Killing-Yano forms with torsion
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• Hidden symmetries of black holes in five-dimensional supergravity
• Chaos in a generalized Euler's three-body problem
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• Spinning exact solutions with Sasakian structure in Gauss-Bonnet Maxwell gravity
• Non-compact manifolds with Killing spinors
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