Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric spacetimes
- ZARM, Universitaet Bremen, Am Fallturm, 28359 Bremen (Germany)
- Institut fuer Physik, Universitaet Oldenburg, 26111 Oldenburg (Germany)
The complete analytical solutions of the geodesic equation of massive test particles in higher dimensional Schwarzschild, Schwarzschild-(anti)de Sitter, Reissner-Nordstroem and Reissner-Nordstroem-(anti)de Sitter spacetimes are presented. Using the Jacobi inversion problem restricted to the theta divisor the explicit solution is given in terms of Kleinian sigma functions. The derived orbits depend on the structure of the roots of the characteristic polynomials which depend on the particle's energy and angular momentum, on the mass and the charge of the gravitational source, and the cosmological constant. We discuss the general structure of the orbits and show that due to the specific dimension-independent form of the angular momentum and the cosmological force a rich variety of orbits can emerge only in four and five dimensions. We present explicit analytical solutions for orbits up to 11 dimensions. A particular feature of Reissner-Nordstroem spacetimes is that bound and escape orbits traverse through different universes.
- OSTI ID:
- 21251142
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 78, Issue 12; Other Information: DOI: 10.1103/PhysRevD.78.124018; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Unstable circular null geodesics of static spherically symmetric black holes, Regge poles, and quasinormal frequencies
Analytical solution of the geodesic equation in Kerr-(anti-) de Sitter space-times