  We analyse the impact of positivity conditions on static spherically
symmetric deformations of the Schwarzschild space-time. The metric is taken to
satisfy, at least asymptotically, the Einstein equation in the presence of a
non-trivial stress-energy tensor, on which we impose various physicality
conditions. We systematically study and compare the impact of these conditions
on the space-time deformations. The universal nature of our findings applies to
both classical and quantum metric deformations with and without event horizons.
We further discuss minimal realisations of the asymptotic stress energy tensor
in terms of physical fields. Finally, we illustrate our results by discussing
concrete models of quantum black holes.
