  Analytic approximations for the stress-energy of quantized fields in the
Hartle-Hawking state in static black hole spacetimes predict divergences on the
event horizon of the black hole for a number of important cases. Such
divergences, if real, could substantially alter the spacetime geometry near the
event horizon, possibly preventing the black hole from existing. The results of
three investigations of these types of effects are presented. The first
involves a new analytic approximation for conformally invariant fields in
Reissner-Nordstrom spacetimes which is finite on the horizon. The second
focuses on the stress-energy of massless scalar fields in Schwarzschild-de
Sitter black holes. The third focuses on the stress-energy of massless scalar
fields in zero temperature black hole geometries that could be solutions to the
semiclassical backreaction equations near the event horizon of the black hole.
