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arXiv · 1608.05116

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

B. Harms·A. Stern
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Abstract

We obtain numerical solutions for rotating topological solitons of the nonlinear $σ$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $σ$-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.

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B. Harms, A. Stern. 2016-10-15. Spinning $σ$-model solitons in $2+1$ Anti-de Sitter space. https://doi.org/10.1016/j.physletb.2016.10.075

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