Slow dynamos in Lorentz tori Anti-de Sitter spacetime embedded in Riemann 2D-space

Abstract

Earlier Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have shown that a fast dynamo in compact two-dimensional manifold can be supported as long as its Riemannian curvature be negative. Recently Klebanov and Maldacena [Phys Today (2008)] showed that a similar flat spacetime embedding of a 2D negative Riemannian hyperbolic embedding in 2+1-D space-time, is achieved by a coordinate transformation. This embedding is used here to obtain a flat spacetime embedding of a slow dynamo in Riemannian 2D compact manifold of negative constant curvature. In is shown that a slow dynamo appears in anti-de Sitter space (AdS) Lorentz tori. This is in agreement with Bassett et al [Phys Rev D (2001)] cosmic dynamo where suppression of resonance by universe expansion slow dynamo action in comparison to preheating phases. Other example of flat embeddings, which keeps some resamblance with AdS slow dynamo, is given by the embedding of Moebius strip [Shukurov, Stepanov, Sokoloff, PRE (2008)] in the laboratory.