Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius
General Relativity and Quantum Cosmology
2016-02-24 v1
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 , lying on a Euclidean two--plane. Then we outline an alternative proof for . We also make a comment on the shape of timelike geodesics in de Sitter space.
Keywords
Cite
@article{arxiv.1602.07111,
title = {Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius},
author = {Leszek M. Sokołowski and Zdzislaw A. Golda},
journal= {arXiv preprint arXiv:1602.07111},
year = {2016}
}
Comments
An expanded version of the work published in International Journal of Modern Physics D. 8 pages, 0 figures