Every timelike geodesic in Anti-de Sitter spacetime is a circle of the same radius
Oct 9, 20156 pages
Published in:
- Int.J.Mod.Phys.D 25 (2015) 01, 1650007
- Published: Oct 9, 2015
e-Print:
- 1602.07111 [gr-qc]
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Abstract: (World Scientific)
In this paper, we refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti-de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by Λ, lying on a Euclidean two-plane. Then, we outline an alternative proof for AdS4. We also make a comment on the shape of timelike geodesics in de Sitter space.Note:
- An expanded version of the work published in International Journal of Modern Physics D. 8 pages, 0 figures
- Anti-de Sitter spacetime
- timelike geodesics
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