The bizarre anti-de Sitter spacetime

TL;DR

This paper explores the unusual geometric and physical properties of anti-de Sitter spacetime, revealing superluminal velocities, infinite energies, and inaccessible regions, emphasizing its mathematical rather than physical nature.

Contribution

It provides an elementary tensor calculus derivation of anti-de Sitter spacetime's bizarre features and explains these phenomena using a five-dimensional embedding space.

Findings

Superluminal velocities of light and particles

Infinite energy required to escape at infinite distance

Existence of inaccessible spacetime regions

Abstract

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 \textit{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.