Speaker
Description
Perturbations around a non-trivial spacetime background encode much of the physics we can extract from it --- the ringdown spectrum of a perturbed black hole, or particles produced in a cosmological background. In both cases the relevant mode equation is treated in the WKB approximation, whose solutions are used to impose boundary conditions on the asymptotic states that fix the quasinormal-mode spectrum or the vacuum/particle content. However, the WKB series is only asymptotic and generically divergent: it is not globally valid and its naive truncation carries an intrinsic ambiguity tied to the Stokes phenomenon. In this talk, using black hole quasinormal modes and cosmological particle production as two concrete examples, I discuss how the exact WKB analysis, the Borel resummation of the WKB series along its associated Stokes graph, removes this ambiguity and yields exact, globally valid quantization conditions. I will highlight the common structure behind both applications, illustrating how the global analytic structure of wave equations encodes physical information beyond a finite-order WKB expansion.