Quantum toy model for black-hole back-reaction

We propose a simple quantum field theoretical toy model for black hole evaporation and study the back-reaction of Hawking radiation onto the classical background. It turns out that the horizon is also ``pushed back'' in this situation (i.e., the interior region shrinks) but this back-reaction is not caused by energy conservation but by momentum balance. The effective heat capacity and the induced entropy variation can have both signs -- depending on the parameters of the model. PACS: 04.62.+v, 04.70.Dy.Comment: 4 page