Abstract: Not all effective field theories are created equal. Some appear perfectly healthy at low energies and yet may contain the seeds of their own inconsistency. Dispersion relations and positivity provide one diagnostic of such inconsistencies. Are there other criteria capable of identifying theories that cannot admit a consistent ultraviolet completion? It has been proposed that a suitable notion of black holes' stability could provide such a criterion. More specifically, quasinormal-modes in EFT extensions of gravity have been argued to decay faster than their GR counterpart, and if not the deviation should remain unresolvable.
I will show that, besides lacking a compelling physical motivation, this proposal contains no information beyond that already encoded in existing positivity constraints, with one curious exception. I will substantiate these claims in the context of GREFT and scalar-tensor theories, using Einstein--dilaton--Gauss--Bonnet and Einstein--Maxwell gravity as explicit examples.