Perturbative calculation of quasinormal modes ofd-dimensional black holes

We study analytically quasinormal modes in a wide variety of black holespacetimes, including $d$--dimensional asymptotically flat spacetimes andnon-asymptotically flat spacetimes (particular attention has been paid to thefour dimensional case). We extend the analytical calculation to includefirst-order corrections to analytical expressions for quasinormal modefrequencies by making use of a monodromy technique. All possible typeperturbations are included in this paper. The calculation performed in thispaper show that systematic expansions for uncharged black holes includedifferent corrections with the ones for charged black holes. This differencemakes them have a different $n$--dependence relation in the first-ordercorrection formulae. The method applied above in calculating the first-ordercorrections of quasinormal mode frequencies seems to be unavailable for blackholes with small charge. This result supports the Neitzke's prediction. On whatconcerns quantum gravity we confirm the view that the $\ln3$ in $d=4$Schwarzschild seems to be nothing but some numerical coincidences.Comment: 49 pages, 5 figure