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

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arxiv 1009.6117 v1 pith:GH6532SV submitted 2010-09-30 gr-qc

Eva Hackmann , Valeria Kagramanova , Jutta Kunz , Claus Lämmerzahl This is my paper
classification gr-qc
keywords orbitssitteranalyticalfunctionsgeodesicsigmaspace-timespace-times
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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.

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Cited by 2 Pith papers

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  1. Topological charge and black hole photon spheres in massive gravity

    gr-qc 2025-09 unverdicted novelty 7.0 of 10

    In dRGT massive gravity, static spherically symmetric black holes exhibit zero, one, or two photon spheres whose topological charges and stability patterns differ from Einstein gravity and from horizonless compact objects.

  2. Optical images of the Kerr-Sen black hole and thin accretion disk

    gr-qc 2025-07 reject novelty 3.0 of 10

    Ray-traced images of a Kerr-Sen black hole with a thin accretion disk show spin-dominated inner-shadow deformation and inclination-dominated redshift maps, while the 86-versus-230 GHz brightness gap is inherited from ...

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