We study scalar, electromagnetic, axial, and polar gravitational perturbations of the four-dimensional Reissner-Nordström-like black holes with a tidal charge in the Randall-Sundrum braneworld in the first approximation when the tidal perturbations are not taken into account. The quasinormal modes of these 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 all kinds of perturbations. Moreover, we determine the greybody factor, giving transmission and reflection of the scattered waves through the effective potentials. It has been shown that the scalar perturbative fields are the most favorite to reflect the wave as compared to the other fields. With increasing value of the tidal charge, the 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-Nordström black holes.

• Received 2 May 2016

DOI:https://doi.org/10.1103/PhysRevD.93.124017