Classical solutions of gravitating Chern - Simons electrodynamics ∗
نویسنده
چکیده
We discuss the reduction of gravitating Chern-Simons electrodynamics with two commuting Killing vectors to a dynamical problem with four degrees of freedom, and present regular particle-like solutions. In three space-dimensions, the abelian Higgs model coupled to Einstein gravity is known to admit static multi-vortex solutions [1]. Stationary vortex solutions arise [2] when a Chern-Simons term for the gauge field [3, 4] is added. We shall show here that, in this last case, the Higgs field is not really necessary, as sourceless gravitating Chern-Simons electrodynamics admits regular particle-like solutions. In the present talk, we first discuss the reduction of gravitating ChernSimons electrodynamics with two commuting Killing vectors to a dynamical problem. We then present exact particle-like solutions to this problem in the case where the cosmological constant is negative. Finally, we briefly discuss the generalization to the case where Einstein gravity is replaced by topologically massive gravity [4]. ∗invited talk at the workshop on Geometry of Constrained Dynamical Systems, Cambridge 15-18 June 1994
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