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In this paper the generalization of the Gribov pendulum equation in theCoulomb gauge for curved spacetimes is analyzed on static spherically symmetricbackgrounds. A rigorous argument for the existence and uniqueness of solutionis provided in the asymptotically AdS case. The analysis of the strong and weakboundary conditions is equivalent to analyzing an effective one-dimensionalSchrodinger equation. Necessary conditions in order for spherically symmetricbackgrounds to admit solutions of the Gribov pendulum equation representingcopies of the vacuum satisfying the strong boundary conditions are given. It isshown that asymptotically flat backgrounds do not support solutions of theGribov pendulum equation of this type, while on asymptotically AdS backgroundssuch ambiguities can appear. Some physical consequences are discussed.

Gribov pendulum in the Coulomb gauge on curved spaces