Quasinormal behavior of the d-dimensional Schwarzshild black hole and higher order WKB approach

We find the low lying scalar quasinormal modes of $d$-dimensional Schwarzshild black hole. It proves that the real part of the complex mode is proportional to the number of dimensions $d$. In addition the WKB formula for computing QN modes, developed to the 3th order beyond the eikonal approximation, is extended to the 6th order here. This gives us accurate and economic way to compute the quasinormal frequencies. The asymptotic formula for large multipole number $l$ and arbitrary $d$ is derived.