Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-07-08
Phys.Rev.D78:102002,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, 10 figures
Scientific paper
10.1103/PhysRevD.78.102002
I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).
No associations
LandOfFree
Spacetime Encodings II - Pictures of Integrability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spacetime Encodings II - Pictures of Integrability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spacetime Encodings II - Pictures of Integrability will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-268321