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Persistent puzzles to do with information loss for black holes havestimulated critical reassessment of the domain of validity of semiclassical EFTreasoning in curved spacetimes, particularly in the presence of horizons. Weargue here that perturbative predictions about evolution for very long timesnear a horizon are subject to problems of secular growth - i.e. powers of smallcouplings come systematically together with growing functions of time. Suchgrowth signals a breakdown of naive perturbative calculations of late-timebehaviour, regardless of how small ambient curvatures might be. Similar issuesof secular growth also arise in cosmology, and we build evidence for the casethat such effects should be generic for gravitational fields. In particular,inferences using free fields coupled only to background metrics can bemisleading at very late times due to the implicit assumption they make ofperturbation theory when neglecting other interactions. Using the Rindlerhorizon as an example we show how this secular growth parallels similarphenomena for thermal systems, and how it can be resummed to allow late-timeinferences to be drawn more robustly. Some comments are made about theappearance of an IR/UV interplay in this calculation, as well as on thepossible relevance of our calculations to predictions near black-hole horizons.

Failure of Perturbation Theory Near Horizons: the Rindler Example