Gravitating Chern-Simons vortices

TL;DR

This paper constructs and analyzes exact self-dual vortex solutions in a Chern-Simons-Higgs model coupled to Einstein gravity in 2+1 dimensions, revealing conditions for regular, causally well-behaved spacetimes.

Contribution

It derives a family of doubly self-dual vortex solutions and simplifies the self-duality condition to a single metric assumption.

Findings

Exact vortex solutions interpolate between vacua.

Solutions require negative gravitational constant for regularity.

Spacetimes are free of closed timelike curves under certain conditions.

Abstract

The construction of self-dual vortex solutions to the Chern-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.