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We study null and timelike constant radii geodesics in the environment of anover-spinning putative Kerr-type naked singularity. We are particularlyinterested in two topics: first, the differences of the shadows of the nakedrotating singularity and the Kerr black hole; and second, the spinning downeffect of the particles falling from the accretion disk. Our findings are asfollows: around the naked singularity, the non-equatorial prograde orbits inthe Kerr black hole remain intact up to a critical rotation parameter($\alpha=\frac{4\sqrt{2}}{3\sqrt{3}}$) and cease to exist above this value.This has an important consequence in the shadow of the naked singularity if theshadow is registered by an observer on the rotation plane or close to it as theshadow cannot be distinguished from that of a Kerr black hole viewed from thesame angle. We also show that the timelike retrograde orbits in the equatorialplane immediately (after about an 8\% increase in mass) reduce the spinparameter of the naked singularity from larger values to $\alpha=1$ at which anevent horizon appears. This happens because the retrograde orbits have a largercapture cross-section than the prograde ones. So if a naked singularity happensto have an accretion disk, it will not remain naked for long, an event horizonforms.

Instability of a Kerr-type naked singularity due to light and matter accretion and its shadow