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arXiv · 1602.07111

Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius

Leszek M. Sokołowski·Zdzislaw A. Golda
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Abstract

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 $AdS_4$. We also make a comment on the shape of timelike geodesics in de Sitter space.

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Leszek M. Sokołowski, Zdzislaw A. Golda. 2016-02-23. Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius. https://doi.org/10.1142/s0218271816500073

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