Constraints on the Geometries of Black Holes in Classical and Semiclassical Gravity

Constraints on the geometries of static spherically symmetric black holes are obtained by requiring that the spacetime curvature be analytic at the event horizon. Further constraints are obtained by requiring that the semiclassical trace equation be satisfied in the case that only conformally invariant fields are present. It is found that there exists a range of sizes for which zero temperature black holes do not exist. The range depends on the number and types of quantized fields present.