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 to do not approach to the well-known value T-H ln 3 but approach to TH ln k(n), where k(n) is a number dependent on the extra dimensions. For the scalar field perturbation Re(omega/ T-H) = ln 3 is reproduced when n = 0. For n not equal 0, however, Re(omega/ T-H) is smaller than ln 3. It is shown also that when n > 4, Im(omega/T-H) vanishes in the scalar field perturbation. For the gravitational perturbation it is shown that Re(omega)/T-H) = ln 3 is reproduced when n = 0 and n = 4. For different n, however, Re(omega/T-H) is smaller than ln 3. When n = infinity, for example, Re(omega/T-H) approaches to ln(1 + 2 cos root 5 pi) approximate to 0.906. Unlike the scalar field perturbation lm(omega/TH) does not vanish regradless of the number of extra dimensions. (c) 2005 Elsevier B.V. All rights reserved.