Geodesic equation in Schwarzschild-(anti-)de Sitter space-times: Analytical solutions and applications

Journal Article · Tue Jul 15 04:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.024035· OSTI ID:21250385

Hackmann, Eva; Laemmerzahl, Claus ^[1]

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1. ZARM, University of Bremen, Am Fallturm, 28359 Bremen (Germany)

The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer anomaly is addressed. The periastron shift and its post-Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space-times.

• OSTI ID: 21250385
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 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
FUNCTIONS
ORBITS
SCHWARZSCHILD METRIC
SPACE-TIME