Pure Lovelock black holes in dimensions d=3N+1 are stable

In this paper, we show that pure Lovelock static Schwarzschild's analogue black holes in dimensions d>3N+1, where N is the degree of Lovelock polynomial action, are stable even though pure Gauss-Bonnet N=2 black holes are unstable in dimensions d<7. We also discuss and compare quasinormal modes for pure Lovelock and the corresponding Einstein black hole in the same dimension. We find that perturbations decay with a characteristic time which is weakly dimensional dependent as it depends only on the gravitational potential of the background solution, while the frequency of oscillations depend on the dimension. Also, we show that the spectrum of perturbations is not isospectral except in d=4.