Asymptotic quasinormal frequencies of brane-localized black hole

The asymptotic quasinormal frequencies of the brane-localized (4+n)-dimensional black hole are computed. Since the induced metric on the brane is not an exact vacuum solution of the Einstein equation defined on the brane, the real parts of the quasinormal frequencies ω do not approach to the well-known value THln3 but approach to THlnkn, where kn is a number dependent on the extra dimensions. For the scalar field perturbation Re(ω/TH)=ln3 is reproduced when n=0. For n≠0, however, Re(ω/TH) is smaller than ln3. It is shown also that when n>4, Im(ω/TH) vanishes in the scalar field perturbation. For the gravitational perturbation it is shown that Re(ω/TH)=ln3 is reproduced when n=0 and n=4. For different n, however, Re(ω/TH) is smaller than ln3. When n=∞, for example, Re(ω/TH) approaches to ln(1+2cos5π)≈0.906. Unlike the scalar field perturbation Im(ω/TH) does not vanish regradless of the number of extra dimensions.