Existence of the self-graviting Chern-Simons vortices

Abstract

We prove existence of multivortex solutions of the self-dual Einstein-Chern-Simons-Higgs system, proposed by Clement [Phys. Rev. D 54, 1844-1847 (1996)]. We consider both the topological and the nontopological boundary conditions for open, conformally flat manifolds. For nontopological boundary conditions we use perturbation argument from a solution of the Liouville equation combined with the implicit function theorem. Using this argument we have existence for arbitrary positive number for the gravitational constant. For topological boundary condition we construct solutions for small gravitational constant by using the super/subsolution method. For sufficiently large gravitational constant we have a nonexistence result for the radially symmetric topological solutions. We also obtain the decay estimates near infinity for both of the topological and the nontopological solutions. (C) 2003 American Institute of Physics.