2004/05/31 by G. V. Kraniotis, G V Kraniotis · 2 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #astro-ph #gr-qc
paper · pdf · doi:10.1088/0264-9381/21/19/016
published as Class. Quantum Grav. 21 (2004) 4743-4769 · 37 pages,LaTeX, Published in Classical and Quantum Gravity 21 (2004) 4743-4769
openalex publication_date 2004/09/22 · arxiv created 2004/10/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The timelike geodesic equations resulting from the Kerr gravitational metric element are derived and solved exactly including the contribution from the cosmological constant. The geodesic equations are derived, by solving the Hamilton-Jacobi partial differential equation by separation of variables. The solutions can be applied in the investigation of the motion of a test particle in the Kerr and Kerr-(anti) de Sitter gravitational fields. In particular, we apply the exact solutions of the timelike geodesics i) to the precise calculation of dragging (Lense-Thirring effect) of a satellite's spherical polar orbit in the gravitational field of Earth assuming Kerr geometry, ii) assuming the galactic centre is a rotating black hole we calculate the precise dragging of a stellar polar orbit aroung the galactic centre for various values of the Kerr parameter including those supported by recent observations. The exact solution of non-spherical geodesics in Kerr geometry is obtained by using the transformation theory of elliptic functions. The exact solution of spherical polar geodesics with a nonzero cosmological constant can be expressed in terms of Abelian modular theta functions that solve the corresponding Jacobi's inversion problem.