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We study massless scalar theory with the quartic self-interacting term faraway from and near to evaporating and spherically symmetric black hole. Wepropose a principle of how to define the physical notion of particle in curvedspace-time. Employing this definition, we compute one-loop correction to theself-energy and coupling constant of the scalar field near the horizon in thefreely-falling frame. We find that the coupling constant becomes slightlystronger near to the horizon. We also find that the term in the 2-pointfunction that is (partially) responsible for the black-hole evaporationcorresponds to the sub-leading correction to the Feynman propagator whose polestructure is of the leading order.

Near-horizon physics of an evaporating black hole: One-loop effects in the \lambda\Phi^4-theory