Hello Doug,
Thanks for your reply; you don't need to apologize for its length! Sorry for not replying earlier; I've been distracted by various extraneous issues.
At any rate, there's one thing that still puzzles me. I grant your point about the horizon radius increasing with the energy scale. What I'm not sure about is whether this point is applicable to the case of an evaporating black hole, in which the black hole's mass M goes to zero. For, as the horizon radius grows, it would seem that M increases, so that we're not dealing with an evaporating black hole at all. Or, if evaporation does occur here, it (arguably) happens "all at once" in a sudden burst of radiation that reflects instability of the black hole at (or below?) the Planck scale; and this doesn't seem to fit your model of an evaporation process characterized by self-similarity. Such an instability leading to evaporation is mentioned on p. 4 of Spallucci and Ansoldi's "Regular black holes in UV self-complete quantum gravity" (arXiv:1101.2760), in which the authors note the positive correlation between horizon size and energy scale. They address the above instability by arguing that the Planck scale represents a minimal size for black holes, which are stable with respect to this scale. In other words, they conclude that the horizon/energy correlation is associated with stable black holes of minimal size, rather than with evaporating black holes -- which brings us back to my question above concerning the (im)possibility of using this correlation in the case of evaporating black holes.
I apologize if I'm missing something here, or if I've misunderstood your ideas.
Thanks again for your reply.
-Willard