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GR: Fachverband Gravitation und Relativitätstheorie

GR 13: Klassische Allgemeine Relativitätstheorie 1

GR 13.1: Vortrag

Donnerstag, 18. März 2010, 09:10–09:30, JUR K

Analytic solution of the geodesic equations in the Plebański-Demiański spacetimes of generalized Black Holes — Eva Hackmann², Valeria Kagramanova¹, Jutta Kunz¹, and •Claus Lämmerzahl² — ¹Universität Oldenburg — ²ZARM, Universität Bremen

The Plebański–Demiański metric represents the complete family of Petrov type D solutions of the Einstein-Maxwell equations in 4 dimensions with an aligned electromagnetic field and non-zero cosmological constant. It includes e.g. Kerr-de Sitter, NUT-de Sitter and Kerr–NUT–de Sitter spacetimes. These spacetimes are characterized by 7 parameters: mass, nut parameter, rotation parameter, electric and magnetic charges, cosmological constant and the acceleration. We show that the separable Hamilton–Jacobi equations in the spacetimes without acceleration are analytically integrable and present the complete sets of analytic solutions of the equation of motion for a charged particle. The solutions are given in terms of the Kleinian sigma functions and are based on the theory of hyperelliptic integrals and functions.