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

摘要

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., 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.