Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times
Abstract
We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic functions. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the ``Misner string'' in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub [C. W. Misner and A. H. Taub, Sov. Phys. JETP 28, 122 (1969) [C. W. MisnerA. H. TaubZh. Eksp. Teor. Fiz. 55, 233 (1968)]], and the analytic extension of Miller, Kruskal and Godfrey [J. G. Miller, M. D. Kruskal, and B. Godfrey, Phys. Rev. D 4, 2945 (1971)], and compare with the Reissner-Nordstr\"om space-time.