Accurate quasinormal modes of the five-dimensional Schwarzschild-Tangherlini black holes

The objective of this paper is to construct the accurate (say, 11 decimal places) frequencies quasinormal modes five-dimensional Schwarzschild-Tangherlini black hole using three major techniques: Hill determinant method, continued fractions and WKB-Pad\'e method discuss limitations each. It shown that for massless scalar, gravitational tensor, vector, electromagnetic vector perturbations considered in paper, (both with convergence acceleration) always give identical results, whereas gives results are amazingly most cases. Notable exception ($j=2$ $\ensuremath{\ell}=2$), which approach apparently does not work. Here we have an interesting situation WKB-based methods (WKB-Pad\'e WKB--Borel--Le Roy) complex frequency differs from result obtained within framework fraction method. For fundamental mode, deviation real part exact value 0.5% imaginary 2.7%. $\ensuremath{\ell}\ensuremath{\ge}3$ accuracy WKB similar again other perturbations. case scalar briefly discussed.