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 ωTH−1→log 3+ 2πi(n+1/2) as n→∞, where ω, TH, and n are the oscillation frequency, the Hawking temperature of the black hole, and the mode number, respectively.