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

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 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.