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The retarded Green function for linear field perturbations in Schwarzschildblack hole space-time possesses a branch cut in the complex-frequency plane.This branch cut has remained largely unexplored: only asymptotic analyseseither for small-frequency (yielding the known tail decay at late times of aninitial perturbation of the black hole) or for large-frequency (quasinormalmodes close to the branch cut in this regime have been linked to quantumproperties of black holes) have been carried out in the literature. The regimealong the cut inaccessible to these asymptotic analyses has so far remainedessentially unreachable. We present a new method for the analytic calculationof the branch cut directly on the cut for general-spin fields in Schwarzschildspace-time. This method is valid for any values of the frequency on the cut andso it provides analytic access to the whole branch cut for the first time. Wecalculate the modes along the cut and investigate their properties andconnection with quasinormal modes. We also investigate the contribution fromthese branch cut modes to the self-force acting on a point particle on aSchwarzschild background space-time.

Analytic Investigation of the Branch Cut of the Green Function in Schwarzschild Space-time