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GR: Fachverband Gravitation und Relativitätstheorie
GR 11: Hauptvorträge Schwarze Löcher und Felder (gemeinsam mit MP)
GR 11.2: Invited Talk
Wednesday, February 29, 2012, 17:15–17:45, ZHG 002
Analytical approach to the geodesic equations in General Relativity — Victor Enolski2,3,4, Eva Hackmann4, •Valeria Kagramanova1, Jutta Kunz1, and Claus Lämmerzahl4 — 1Institut für Physik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg — 2Hanse-Wissenschaftskolleg (HWK), 27733 Delmenhorst, Germany — 3Institute of Magnetism, 36-b Vernadsky Blvd, Kyiv 03142, Ukraine — 4ZARM, Universität Bremen, Am Fallturm, ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen, German
The motion of test particles and light is of great importance for the investigation of the physical properties of gravitational fields since only matter and light can be observed. There are two main methods to solve the geodesic equations: analytical and numerical. Analytical solutions deliver an exact solution of the equations of motion, have arbitrary accuracy and allow to investigate the properties of the motion and hence of the gravitating body itself in detail. In this talk we present the analytical solution of the geodesic equation in many well-known black hole space-times. In particular, in the Plebanski-Demianski space-time of generalized black holes. The solution is expressed in terms of the Weierstrass' elliptic or Abelian hyperelliptic functions. That depends on the degree of difficulty of the considered problem and on the number of parameters characterizing the black hole and the test particle. We integrate differentials of all three kind with arbitrary genus of the underlying polynomial curve. We also present the analytical expressions for the observable quantities such as perihelion shift for planetary orbits and light deflection for escape orbits of photons.