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GR: Fachverband Gravitation und Relativitätstheorie

GR 21: Numerische Relativitätstheorie

GR 21.1: Vortrag

Freitag, 2. März 2012, 14:00–14:20, ZHG 002

Conservation laws and evolution schemes in geodesic, hydrodynamic and magnetohydrodynamic flows — •Charalampos Markakis^1,2, Koji Uryu³, Eric Gourgoulhon⁴, and Jean-Philippe Nicolas⁵ — ¹Theoretical Physics Institute, University of Jena, Germany — ²Department of Physics, University of Wisconsin - Milwaukee, USA — ³Department of Physics, University of the Ryukyus, Okinawa, Japan — ⁴LUTh, Paris Observatory, Meudon, France — ⁵Department of Mathematics, University of Western Brittany, Brest, France

Carter, Arnold and others have shown that the elements of a perfect barotropic fluid obey particle-like laws of motion that can be expressed in covariant form and derived from simple variational principles. This framework can accommodate neutral or poorly conducting charged fluids. We extend this framework to perfectly conducting fluids via the Bekenstein-Oron description of ideal MHD. This allows one to cast the ideal MHD equations into a circulation-preserving hyperbolic form. In this framework, conserved circulation integrals, such as those of Alfven, Kelvin and Bekenstein-Oron, emerge simply as special cases of the Poincare-Cartan integral invariant of Hamiltonian systems. Such scheme can be used to evolve oscillating stars or radiating binaries with magnetic fields in numerical relativity.

Synge and Lichnerowicz have further shown that barotropic fluid flow may be represented as geodesic flow in a conformally related manifold. By extending the notion of a metric to allow for Finsler geometries, we generalize this result to ideal MHD.