Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric spacetimes

Journal Article · Mon Dec 15 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.124018· OSTI ID:21251142

Hackmann, Eva; Laemmerzahl, Claus ^[1]; Kagramanova, Valeria; Kunz, Jutta ^[2]

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1. ZARM, Universitaet Bremen, Am Fallturm, 28359 Bremen (Germany)
2. 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, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 78; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
ANGULAR MOMENTUM
COSMOLOGICAL CONSTANT
DE SITTER GROUP
EQUATIONS
MASS
METRICS
POLYNOMIALS
SIGMA MODEL
SPACE-TIME
TEST PARTICLES
UNIVERSE