Failure of Perturbation Theory Near Horizons: the Rindler Example

TL;DR

This paper demonstrates that perturbation theory near horizons, such as Rindler horizons, suffers from secular growth issues at late times, which can be mitigated through resummation techniques, impacting black hole information loss debates.

Contribution

It reveals the breakdown of naive perturbative methods near horizons due to secular growth and proposes resummation as a solution, with implications for black hole physics and cosmology.

Findings

Secular growth causes perturbation theory to fail at late times near horizons.

Resummation techniques can restore the validity of late-time predictions.

Similar secular effects are likely in cosmological and gravitational contexts.

Abstract

Persistent puzzles to do with information loss for black holes have stimulated critical reassessment of the domain of validity of semiclassical EFT reasoning in curved spacetimes, particularly in the presence of horizons. We argue here that perturbative predictions about evolution for very long times near a horizon are subject to problems of secular growth - i.e. powers of small couplings come systematically together with growing functions of time. Such growth signals a breakdown of naive perturbative calculations of late-time behaviour, regardless of how small ambient curvatures might be. Similar issues of secular growth also arise in cosmology, and we build evidence for the case that such effects should be generic for gravitational fields. In particular, inferences using free fields coupled only to background metrics can be misleading at very late times due to the implicit assumption they make of perturbation theory when neglecting other interactions. Using the Rindler horizon as an example we show how this secular growth parallels similar phenomena for thermal systems, and how it can be resummed to allow late-time inferences to be drawn more robustly. Some comments are made about the appearance of an IR/UV interplay in this calculation, as well as on the possible relevance of our calculations to predictions near black-hole horizons.