Radial and vertical epicyclic frequencies of Keplerian motion in the field of Kerr naked singularities. Comparison with the black hole case and possible instability of naked-singularity accretion discs

摘要: 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 microquasars can be explained by associated resonant or trapping effects. Because growing theoretical evidence possible existence naked singularities, we discuss behaviour fundamenal for motion field primarily order to find phenomena that could observationally distinguish a hypothetical singularity from holes. Some astrophysically consequences are sketched, namely strong all with radial equal given relation $\omega_\mathrm{sr}\,$=$\,\,a^{-2}\sqrt {a^2-1}\,(a^2+1 )^{-1}$.