Paradoxes before the paradox: setting up the information loss problem

The information loss paradox is widely regarded as one of the biggest open problems in theoretical physics. Several classical and quantum features must be present to enable its formulation. First, an event horizon is needed to justify the objective status of tracing out degrees of freedom inside the black hole. Second, evaporation must be completed (or nearly completed) in finite time according to a distant observer, and so the formation of the black hole also should occur in finite time. In spherical symmetry these requirements constrain the possible metrics strongly enough to obtain a unique formation scenario and match their parameters with the semiclassical results. However, the two principal generalizations of the Hawking temperature on the dynamic background do not agree with each other, and neither can correspond to the emission of nearly-thermal radiation. We infer from this that the information loss problem cannot be posed in its standard form.