A WKB approach to scalar fields dynamics in curved space-time

TL;DR

This paper introduces a WKB-based method to analyze scalar field dynamics in curved space-times, providing improved physical insights and accurate calculations of greybody factors and energy levels in black hole and AdS backgrounds.

Contribution

A novel WKB approximation scheme is developed for scalar fields in curved space-times, enhancing understanding and computational accuracy in black hole and AdS scenarios.

Findings

Rederived greybody factors for evaporating black holes.

Accurately computed scalar field energy levels in AdS space.

Investigated stationary solutions in Schwarzschild-AdS background.

Abstract

Quantum fields exhibit non-trivial behaviours in curved space-times, especially around black holes or when a cosmological constant is added to the field equations. A new scheme, based on the Wentzel-Kramers-Brillouin (WKB) approximation is presented. The main advantage of this method is to allow for a better physical understanding of previously known results and to give good orders of magnitude in situations where no other approaches are currently developed. Greybody factors for evaporating black holes are rederived in this framework and the energy levels of scalar fields in the Anti-de Sitter (AdS) spacetime are accurately obtained. Stationary solutions in the Schwarzschild-Anti-de Sitter (SAdS) background are investigated. Some improvements and the basics of a line of thought for more complex situations are suggested.