Models of evaporating black holes. I

Classical spacetimes which contain evaporating black holes (EBH's) are constructed using the Vaidya metric. These model EBH spacetimes are spherically symmetric, asymptotically flat, and contain event horizons which terminate after finite duration. These model EBH spacetimes are then used as fixed backgrounds for particle-creation calculations, in an attempt to learn something of the dynamics of real, semiclassical EBH spacetimes while bypassing the difficulties associated with the back-reaction problem. The stress-energy tensor of a quantized massless scalar field is studied on the two-dimensional EBH spacetimes obtained by setting $d\theta =d\phi =0\mathrm{}$. If $\lim \left(\frac{\mathrm{dM}}{\mathrm{dv}}\right)\ne 0$ as $M\to 0$ ($v$ the usual ingoing null coordinate), then an infinite flux of outgoing radiation is produced along the Cauchy horizon of the EBH. This behavior suggests that a correct, self-consistent semiclassical EBH spacetime must have $\lim \left(\frac{\mathrm{dM}}{\mathrm{dv}}\right)=0\mathrm{}$ as $M\to 0$, contrary to the behavior deduced by naively extrapolating Hawking's result all the way down to $M=0\mathrm{}$, which gives $\frac{\mathrm{dM}}{\mathrm{dv}}\sim M^{-2\mathrm{}}$. It also shows that not all zero-mass naked singularities left at the end point of an evaporating black hole are benign; they may produce a divergent flux of created particles.