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THE GREEN FUNCTION OF THE KLEIN–GORDON EQUATION IN BLACK-HOLE COORDINATES
Preview AbstractThe Green function of the Klein–Gordon equation in black-hole coordinates is calculated. This function is a sum on the harmonic modes of the sphere. The first term is a double integration on the spectrum of energy, and the momentum of the particle. Far from the horizon, the double integration is approximated by an integration on a line defined by the relation of energy and momentum of a free particle. Assumptions of time-independence and radial symmetry are made.