Quasinormal behavior of the D -dimensional Schwarzschild black hole and the higher order WKB approach

We study characteristic (quasinormal) modes of a D-dimensional Schwarzschild black hole. It is shown that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\ensuremath{\sim}{\mathrm{Dr}}_{0}^{\ensuremath{-}1}.$ The asymptotic formula for large multipole number l and arbitrary D is derived. In addition, the WKB formula for computing QN modes, developed to the third order beyond the eikonal approximation, is extended to the sixth order here. This gives us an accurate and economic way to compute quasinormal frequencies.