Geometrically Induced Semiclassical Limit for Quasinormal Modes and Greybody Factors in Higher-Dimensional Near-Ultracold spacetimes

Abstract

In this work, we investigate the correspondence between quasinormal modes (QNMs) and greybody factors (GBFs) in higher-dimensional Reissner--Nordstöm--de Sitter black holes based on the massless scalar field. Our analysis focuses on the QNMs in the near-ultracold family where the inner, outer, and cosmological horizons are close together. Under the geometric limit condition, the leading-order Wentzel--Kramers--Brillouin term of the QNM is dominant for fixed angular quantum numbers and dimensionality without imposing the eikonal limit. Particularly, the corresponding GBFs also retain the explicit form of both parameters. Furthermore, we demonstrate that the half-transmission frequency of the GBF and its derivative are related to null geodesics, in terms of aspects such as the angular frequency and Lyapunov exponent, with the use of both parameters. We provide their relationships in arbitrary dimensionality. Furthermore, the higher-order corrections to the QNMs are investigated at the Nariai limit and in the near-ultracold geometry with separated horizons.