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

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 from 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.