2016/11/03 by Leszek M. Sokolowski
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1142/s0219887816300166
published as International Journal of Geometric Methods in Modern Physics 13 no.9 (2016) 1630016 · 31 pages, 3 figures
arxiv created 2016/11/03 · arxiv updated 2016/11/04
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we derive ab initio\/ all these properties and show that they are really weird. One finds superluminal velocities of light and particles, infinite particle energy necessary to escape at infinite distance and spacetime regions inaccessible by a free fall, though reachable by an accelerated spaceship. Radial timelike geodesics are identical to the circular ones and actually all timelike geodesics are identical to one circle in a fictitious five--dimensional space. Employing the latter space one is able to explain these bizarre features of anti--de Sitter spacetime; in this sense the spacetime is not self--contained. This is not a physical world.