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

摘要

We refine and analytically prove an old proposition due to Calabi and Markuson the shape of timelike geodesics of anti--de Sitter space in the ambient flatspace. We prove that each timelike geodesic forms in the ambient space a circleof the radius determined by $\Lambda$, lying on a Euclidean two--plane. Then weoutline an alternative proof for $AdS_4$. We also make a comment on the shapeof timelike geodesics in de Sitter space.