Jena 2013 – wissenschaftliches Programm
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GR: Fachverband Gravitation und Relativitätstheorie
GR 13: Klassische Allgemeine Relativitätstheorie II
GR 13.6: Vortrag
Donnerstag, 28. Februar 2013, 15:30–15:45, HS 6
Action-Angle Variables and KAM Theory in General Relativity — •Daniela Kunst1, Volker Perlick1, and Claus Lämmerzahl1,2 — 1Center of Applied Space Technology and Microgravity (ZARM), University of Bremen — 2University of Oldenburg
Dynamical systems can be described by the Hamiltonian formalism providing the description of the evolution of the system with time. Roughly speaking, they can be classified into integrable and non-integrable systems, where the integrable ones are rather special cases. Nevertheless, it is useful to study such systems since many non-integrable systems can be characterised as a perturbation affecting an integrable system. Using the characteristic property of the foliation of the phase space into n-dimensional tori for integrable systems with n degrees of freedom, it is possible to draw conclusions about the dynamics and the stability behaviour of perturbed integrable systems. This method is based on the classical Kolmogorov-Arnold-Moser Theorem which states that under certain non-degneracy conditions for the integrable Hamiltonian the preservation but slight deformation of particular tori and of the corresponding regular motion is ensured in the perturbed system.
In this talk I present the calculation of action-angle variables in general relativity, in particular for Schwarzschild and Kerr spacetime. Moreover, I discuss the non-degneracy condition for the unperturbed Hamiltonian in Schwarzschild and give and outlook for the application of KAM Theory to general relativistic systems.