This paper examines the effects of interactions on particle emission by black holes. The model used is the $\lambda {\Phi }^4$ interaction for a massless scalar field $\Phi$ in a two-dimensional model for a black-hole space-time and is compared with the calculation for a flat-space model with spatially varying $\lambda$. Although the models suffer from infrared divergences, a number of features of the effect of the interaction on the particle spectrum are discernible. In the absence of any interactions the state of the field is that of a thermal flux of outgoing particles with temperature $T=\frac{1}{8\pi }M$ (the Hawking temperature). If the ingoing state is the vacuum state, the interaction destroys the thermal nature of the outgoing flux. However, if the ingoing flux is thermal with the same temperature as the black hole, detailed balance maintains the thermal character of the outgoing flux. One can regard the ingoing and outgoing fluxes as two separate thermal baths which are coupled by the interaction. If they are at different temperatures, the interaction will destroy the thermal nature of both.

• Received 23 February 1983

DOI:https://doi.org/10.1103/PhysRevD.28.694