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

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 $\Lambda$, lying on a Euclidean two--plane. Then we outline an alternative proof for $Ad{S}_4$. We also make a comment on the shape of timelike geodesics in de Sitter space.

An expanded version of the work published in International Journal of Modern Physics D. 8 pages, 0 figures

References in corpus (1)

• The local and global geometrical aspects of the twin paradox in static spacetimes: I. Three spherically symmetric spacetimes

Cited by in corpus (4)

• The bizarre anti-de Sitter spacetime
• Implications of Kleinian relativity
• Anti-de Sitter relativity
• Physical meaning of the conserved quantities on anti-de Sitter geodesics