Scalar-gravitational perturbations and quasinormal modes in the five dimensional Schwarzschild black hole

We calculate the quasinormal modes (QNMs) for gravitational perturbations of the Schwarzschild black hole in the five dimensional (5D) spacetime with a continued fraction method. For all the types of perturbations (scalar-gravitational, vector-gravitational, and tensor-gravitational perturbations), the QNMs associated with l = 2, l = 3, and l = 4 are calculated. Our numerical results are summarized as follows: (i) The three types of gravitational perturbations associated with the same angular quantum number l have a different set of the quasinormal (QN) frequencies; (ii) There is no purely imaginary frequency mode; (iii) The three types of gravitational perturbations have the same asymptotic behavior of the QNMs in the limit of the large imaginary frequencies, which are given by ωT_H ^-1 → log 3 + 2πi(n + 1/2) as n → ∞, where ω, T_H, and n are the oscillation frequency, the Hawking temperature of the black hole, and the mode number, respectively.