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

## TL;DR

This paper demonstrates the existence of slow dynamo action within Lorentz tori in Anti-de Sitter spacetime, linking geometric embeddings with magnetic dynamo behavior in curved and flat spacetime models.

## Contribution

It introduces a novel flat spacetime embedding of slow dynamos in Riemannian 2D manifolds with negative curvature, specifically in AdS Lorentz tori, connecting geometric embeddings with dynamo theory.

## Key findings

- Slow dynamos are supported in AdS Lorentz tori.
- Embedding of Moebius strip relates to slow dynamo behavior.
- Resonance suppression in expanding universe aligns with slow dynamo action.

## 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.