Black hole temperature: minimal coupling vs conformal coupling

Abstract

In this article, we discuss the propagation of scalar fields in conformally transformed spacetimes with either minimal or conformal coupling. The conformally coupled equation of motion is transformed into a one-dimensional Schr\"{o}dinger-like equation with an invariant potential under conformal transformation. In a second stage, we argue that calculations based on conformal coupling yield the same Hawking temperature as those based on minimal coupling. Finally, it is conjectured that the quasi normal modes of black holes are invariant under conformal transformation.