Quasinormal frequencies of black hole in the braneworld

TL;DR

This paper investigates the quasinormal modes, stability, and wave scattering properties of black holes with tidal charge in the Randall-Sundrum braneworld, revealing their stability and distinctive absorption features compared to standard black holes.

Contribution

It provides the first detailed analysis of scalar, electromagnetic, and gravitational perturbations of braneworld black holes, including quasinormal modes and grey body factors.

Findings

Black holes are stable against perturbations.

Braneworld black holes have larger scalar wave absorption cross sections.

Wave reflection decreases with increasing tidal charge.

Abstract

We have studied scalar, electromagnetic and gravitational perturbations of the four-dimensional Reissner-Nordstr\"{o}m-like black holes with a \textit{tidal charge} in the Randall-Sundrum braneworld. The quasinormal modes of these scalar, electromagnetic, as well as axial and polar gravitational perturbations, have been studied in both normal and eikonal regimes. Calculations have shown that the black holes on the Randall-Sundrum brane are stable against scalar, electromagnetic and gravitational perturbations. Moreover, we determine the grey body factor, giving transmission and reflection of the scattered waves through the scalar, electromagnetic and gravitational effective potentials. It has been shown that the scalar perturbative fields are the most favorite to the reflected as compared to the latter. With increasing value of the tidal charge ability of the all perturbative potentials to reflect the waves decreases. Our calculations in low- and high-frequency regimes have shown that black holes on the braneworld always have a bigger absorption cross section of massless scalar waves than the Schwarzschild and standard Reissner-Nordstr\"{o}m black holes.