Radial and vertical epicyclic frequencies of Keplerian motion in the field of Kerr naked singularities

Relativistic Keplerian orbital frequency ($\nu_{\mathrm{K}}$) and related epicyclic frequencies (radial $\nu_{\mathrm{r}}$, vertical $\nu_{\theta}$) play an important role in the physics of accretion discs orbiting Kerr black holes – quasiperiodic oscillations observed in microquasars can be explained by associated resonant or trapping effects. Because of growing theoretical evidence of the possible existence of naked singularities, we discuss the behaviour of the fundamenal orbital frequencies for Keplerian motion in the field of Kerr naked singularities, primarily in order to find phenomena that could observationally distinguish a hypothetical naked singularity from black holes. Some astrophysically important consequences are sketched, namely the existence of strong resonant frequency for all Kerr naked singularities, with radial and vertical epicyclic frequencies equal and given by the relation $\omega_\mathrm{sr}\,$=$\,\,a^{-2}\sqrt {a^2-1}\,(a^2+1 )^{-1}$.