Long-lived massive scalar modes, grey-body factors, and absorption cross sections of the Reissner--Nordstr\"om-like brane-world black hole

Abstract

We study quasinormal modes, including the quasi-resonant regime, grey-body factors, and absorption cross sections of a massive scalar field in a Reissner--Nordstr\"om-like brane-world black hole endowed with a tidal-charge parameter induced by extra-dimensional effects. Combining semiclassical WKB calculations with time-domain evolution, we determine the range of parameters for which the effective potential keeps the single-barrier shape needed for a reliable quasinormal-mode and scattering analysis. We find that increasing positive tidal charge lowers the barrier, drives the spectrum closer to the quasi-resonant regime, and enhances transmission and absorption, whereas increasing the field mass or multipole number makes the barrier less transparent and shifts absorption to higher frequencies. Our results indicate the onset of an arbitrarily long-lived quasinormal-mode regime. At the same time, this behavior cannot be followed directly in the time-domain profiles, because the asymptotic tails set in too early and mask the late-time ringing.