Spinning $\sigma$-model solitons in $2+1$ Anti-de Sitter space

Abstract

We obtain numerical solutions for rotating topological solitons of the nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $\sigma$-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. Any time slice of the space-time for the type $i)$ solution has a causal singularity, despite the fact that all scalars constructed the curvature tensor are bounded functions. No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singularities. On the other hand, the space-time domain, along with the fields, for the type $ii)$ solutions are singularity free. Multiple families of solutions exhibiting bifurcation phenomena are found for this case.

15 pages, 6 figures

References in corpus (8)

• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Spinning Gravitating Skyrmions
• Towards Skyrmion Stars: Large Baryon Configurations in the Einstein-Skyrme Model
• Hairy AdS Solitons
• Skyrme Black Holes in the Isolated Horizons Formalism
• Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria
• Black Holes with Skyrme Hair
• Topological aspect of black hole with Skyrme hair

Cited by in corpus (3)

• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography
• Rotating AdS Einstein universes from constrained metrics