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

TL;DR

This paper investigates the quasinormal modes, grey-body factors, and absorption cross sections of a massive scalar field around a Reissner--Nordstr"om-like brane-world black hole, revealing how tidal charge and field parameters influence wave behavior.

Contribution

It introduces a combined semiclassical and time-domain approach to analyze scalar field scattering in a brane-world black hole with tidal charge effects, highlighting conditions for long-lived quasinormal modes.

Findings

Increasing tidal charge lowers the potential barrier and enhances absorption.

Higher scalar mass or multipole number reduces transparency and shifts absorption to higher frequencies.

Long-lived quasinormal modes can occur but are masked in late-time signals due to early tails.

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.