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We present here a detailed study of the quasinormal spectrum of brane-localized standard model fields in the vicinity of D-dimensional black holes. A variety of such backgrounds Schwarzschild, Reissner-Nordstr\"om and Schwarzszchild- (anti--) de Sitter are investigated. The dependence of the quasinormal spectra on the dimensionality D, spin of the field s, and multipole number is analyzed. Analytical formulas are obtained for a number of limiting cases: in the limit of large multipole number for Schwarzschild, Schwarzschild-de Sitter, and Reissner-Nordstr\"om black holes, in the extremal limit of the Schwarzschild-de Sitter black hole, and in the limit of small horizon radius in the case of Schwarzschild-anti--de Sitter black holes. We show that an increase in the number of hidden, extra dimensions results in the faster damping of all fields living on the brane, and that the localization of fields on a brane affects the quasinormal spectrum in a number of additional ways, both direct and indirect.
Kanti et al. (Fri,) studied this question.