Gravitating Chern-Simons vortices

The construction of self-dual vortex solutions to the Chem-Simons-Higgs model (with a suitable eighth-order potential) coupled to Einstein gravity in 2+1 dimensions is reconsidered. We show that the self-duality condition may be derived from the sole assumption g(00)=1. Next, we derive a family of exact, doubly self-dual vortex solutions, which interpolate between the symmetrical and asymmetrical vacua. The corresponding spacetimes have two regions at spatial infinity. The eighth-order Higgs potential is positive definite, and closed timelike curves are absent, if the gravitational constant is chosen to be negative.