Analytical solution of the geodesic equation in Kerr-(anti-) de Sitter space-times

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.044020· OSTI ID:21409307

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

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

The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, {zeta}, and {sigma} functions as well as hyperelliptic Kleinian {sigma} functions restricted to the one-dimensional {theta} divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.

• OSTI ID: 21409307
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevD.81.044020; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
ANTI DE SITTER SPACE
COMPARATIVE EVALUATIONS
COSMOLOGICAL CONSTANT
DE SITTER SPACE
EQUATIONS
KERR METRIC
ONE-DIMENSIONAL CALCULATIONS
ORBITS
SPACE-TIME
SPHERICAL CONFIGURATION
TEST PARTICLES
CONFIGURATION
EVALUATION
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
METRICS
SPACE