Semiclassical collapse of a sphere of dust

The semiclassical collapse of a homogeneous sphere of dust is studied. After identifying the independent dynamical variables, the system is canonically quantized and coupled equations describing matter (dust) and gravitation are obtained. The conditions for the validity of the adiabatic (Born-Oppenheimer) and semiclassical approximations are derived. Further, on neglecting back-reaction effects, it is shown that in the vicinity of the horizon and inside the dust the Wightman function for a conformal scalar field coupled to a monopole emitter is thermal at the characteristic Hawking temperature.