Self-force on a scalar point charge in the long throat

An analytic method is presented which allows for the computation of the self-force for a static particle with a scalar charge in the region of an ultrastatic spacetime which one can call the long throat. The method is based on the approximate WKB solution of a radial mode equation for a scalar field. This field is assumed to be massless, with a coupling $ξ$ to the scalar curvature is satisfying the condition $ξ>1/8$.

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