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 the 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 one to characterize Kerr, Taub-NUT, Schwarzschild–de Sitter, or other space-times.

• Received 9 December 2011

DOI:https://doi.org/10.1103/PhysRevD.85.044049