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 Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski and Demia\ifmmode \acute{n}\else \'{n}\fi{}ski 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.

Identifiers

DOI

10.1103/physrevd.85.044049

Citations and references