Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors

DOI10.1063/1.3664754zbMath1273.81068arXiv1107.5987OpenAlexW1977228344WikidataQ125626827 ScholiaQ125626827MaRDI QIDQ2853591

C. Rugina, Gary W. Gibbons

Publication date: 16 October 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.5987

Mathematics Subject Classification ID

Black holes (83C57) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Exact solutions to problems in general relativity and gravitational theory (83C15) Geodesic flows in symplectic geometry and contact geometry (53D25) Equations of motion in general relativity and gravitational theory (83C10) Symmetries and conservation laws in mechanics of particles and systems (70S10) Motion of the gyroscope (70E05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (7)

Ricci-flat spacetimes admitting higher rank Killing tensors ⋮ Eisenhart lift for higher derivative systems ⋮ Conformal killing tensors and covariant Hamiltonian dynamics ⋮ Some metrics admitting nonpolynomial first integrals of the geodesic equation ⋮ Eisenhart lift for Euler's problem of two fixed centers ⋮ Massless geodesics in \(\text{AdS}_5\times Y(p,q)\) as a superintegrable system ⋮ Generalized Lense-Thirring metrics: higher-curvature corrections and solutions with matter

Cites Work

• The Fourier \(U(2)\) group and separation of discrete variables
• Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group
• Invariant characterization of Liouville metrics and polynomial integrals
• Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body
• The Goryachev-Chaplygin gyrostat in quantum mechanics
• Exact solution of the Goryachev-Chaplygin problem in quantum mechanics
• Geometrical classification of Killing tensors on bidimensional flat manifolds
• HIGHER ORDER FIRST INTEGRALS OF MOTION IN A GAUGE COVARIANT HAMILTONIAN FRAMEWORK
• Newton–Hooke spacetimes, Hpp-waves and the cosmological constant
• Kovalevskaya top and generalizations of integrable systems

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