The bizarre anti-de Sitter spacetime

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.

31 pages, 3 figures

References in corpus (5)

• The AdS/CFT Correspondence
• Accelerating black holes in anti-de Sitter universe
• Is AdS stable?
• The local and global geometrical aspects of the twin paradox in static spacetimes: I. Three spherically symmetric spacetimes
• Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius

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• Implications of Kleinian relativity
• The role of an invariant IR cutoff in late time cosmological dynamics
• Anti-de Sitter relativity
• Constraining the Physical State by Symmetries
• Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields
• Physical meaning of the conserved quantities on anti-de Sitter geodesics
• Hawking radiation inside a charged, cosmological black hole
• Non-singular T-K axion stars with/without the dynamical bosonic field in the presence of negative $\Lambda$ term
• Test-field limit of metric nonlinear gravity theories