The Exact WKB analysis and the Stokes phenomena of the Unruh effect and Hawking radiation

TL;DR

This paper applies the exact WKB analysis to the Unruh effect and Hawking radiation, revealing non-perturbative phenomena and Stokes phenomena, and compares these effects with the Schwinger effect and sonic black holes.

Contribution

It introduces a novel application of exact WKB analysis to quantum effects near black holes and accelerations, highlighting non-perturbative phenomena and discrepancies with sonic black holes.

Findings

Stokes phenomena appear in the temporal part of the effects.

Comparison shows discrepancies between black hole radiation and sonic black holes.

Quantum backreactions can be incorporated into the formalism.

Abstract

The physical observables of quantum theory can be described by perturbation theory, which is often given by diverging power series. This divergence is connected to the existence of non-perturbative phenomena, where resurgence allows us to study this connection. Applying this idea to the WKB expansion, the exact WKB analysis gives a clear connection to non-perturbative phenomena. In this paper, we apply the exact WKB analysis to the Unruh effect and Hawking radiation. The mechanism we found in this paper is similar to the Schwinger effect of a constant electric field, where the background is static but the Stokes phenomenon appears in the temporal part. Comparing this with a sonic black hole, our calculations show a clear discrepancy between them. Then, we briefly explain how quantum backreactions can be included in the exact WKB formalism.