It has recently been conjectured that circular trajectories (geodesic as well as non-geodesic) around central compact objects are characterized by the time-to-mass universal lower bound T_{infty }/M>{{mathcal {C}}}, where {T_{infty },M} are respectively the orbital period as measured by flat-space asymptotic observers and the mass of the central compact object, and mathcal{C}=O(1) is a dimensionless constant of order unity. In the present paper we prove that this dimensionless bound is respected by circular orbits around central naked singularities. Intriguingly, it is explicitly proved that the orbital-time-to-mass ratio T_{infty }/M around a central super-spinning singularity remains finite even in the rrightarrow 0 limit of circular orbits with infinitesimally small radial coordinates (which are characterized by a diverging time-to-radius ratio, T_{infty }/rrightarrow infty ). In particular, we reveal the fact that the shortest orbital period around a super-spinning naked singularity is given by the dimensionless relation T_{infty }/M=2pi . In addition, we explore the functional behavior of the time-to-mass ratio of circular trajectories around super-charged (non-vacuum) naked singularities and prove that the dimensionless ratio T_{infty }/M(r) is bounded from below, where M(r) is the gravitational mass contained within the orbital radius of the test particle.
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