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

We study massless scalar theory with the quartic self-interacting term far away from and near to evaporating and spherically symmetric black hole. We propose a principle of how to define the physical notion of particle in curved space-time. Employing this definition, we compute one-loop correction to the self-energy and coupling constant of the scalar field near the horizon in the freely-falling frame. We find that the coupling constant becomes slightly stronger near to the horizon. We also find that the term in the 2-point function that is (partially) responsible for the black-hole evaporation corresponds to the sub-leading correction to the Feynman propagator whose pole structure is of the leading order.