Observables for bound orbital motion in axially symmetric space-times

Abstract

The periastron shift and the Lense-Thirring effect of bound orbital motion in a general axially symmetric space-time given by Plebański and Demiański are analyzed. We also define a measure for the conicity of the orbit and give analytic expressions for all three observables in terms of hyperelliptic integrals and Lauricella's $F_D$ function. For an interpretation of these analytical expressions, we perform a post-Schwarzschild and a post-Newton expansion of these quantities. This clearly shows the influence of the different space-time parameters on the considered observables and allows to characterize Kerr, Taub-NUT, Schwarzschild-de Sitter, or other space-times.

18 pages, revised version

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• The role of elliptic integrals in calculating the gravitational lensing of a charged Weyl black hole surrounded by plasma
• Matter environments around black holes: geodesics, light rings, and ultracompact configurations