Circular orbits around higher dimensional Einstein and pure Gauss-Bonnet rotating black holes

In this paper we study circular orbits around higher dimensional rotating Myers-Perry and pure Gauss-Bonnet (GB) black holes. It turns out that for the former there occurs no potential well to harbour bound and thereby stable circular orbits. The only circular orbits that could occur are all unstable and their radius is bounded from the below by that of the photon circular orbit. On the other hand bound and stable circular orbits do exist for pure GB/Lovelock rotating black holes (the metric is though not an exact solution of pure Lovelock vacuum equation but it satisfies the equation in the leading order and has all the desired properties) in dimensions, $2N+2 \leq D \leq 4N$ (for $N=2$ pure GB in $D = 6, 7, 8$) where $N$ is the degree of Lovelock polynomial. Thus bound and stable circular orbits could exist around higher dimensional rotating black holes only for pure GB/Lovelock gravity. This property is a nice discriminator between Myers-Perry and pure GB/Lovelock rotating black holes.