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

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) space–time 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.