On the Integrability of the Geodesic Flow on a Friedmann-Robertson-Walker Spacetime
| Autor: | Francisco Astorga, J. Felix Salazar, Thomas Zannias |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Geodesic
Integrable system FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Physics - Classical Physics 01 natural sciences General Relativity and Quantum Cosmology symbols.namesake Friedmann–Lemaître–Robertson–Walker metric 0103 physical sciences Invariant (mathematics) 83 Relativity and Gravitation 010303 astronomy & astrophysics Mathematics::Symplectic Geometry Mathematical Physics Mathematical physics Physics Spacetime 010308 nuclear & particles physics Shape of the universe Classical Physics (physics.class-ph) Condensed Matter Physics Atomic and Molecular Physics and Optics Phase space symbols Cotangent bundle Mathematics::Differential Geometry |
| Popis: | We study the geodesic flow on the cotangent bundle of a Friedman-Robertson-Walker spacetime (M, g). On this bundle, the HamiltonJacobi equation is completely separable and this separability leads us to construct four linearly independent integrals in involution i.e. Poisson commuting amongst themselves and pointwise linearly independent. These integrals involve the six linearly independent Killing fields of the background metric g. As a consequence, the geodesic flow on an FRW background is completely integrable in the Liouville-Arnold sense. For the case of a spatially closed universe we construct families of invariant by the flow sub manifolds. 34 pages, no figures |
| Databáze: | OpenAIRE |
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