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Observations of the spin distribution of rapidly rotating neutron stars showevidence for a lack of stars spinning at frequencies larger than $f\approx 700$Hz, well below the predictions of theoretical equations of state. This hasgenerally been taken as evidence of an additional spin-down torque operating inthese systems and it has been suggested that gravitational wave torques may beoperating and be linked to a potentially observable signal. In this paper weaim to determine whether additional spin-down torques are necessary, or whetherthe observed limit of $f\approx 700$ Hz could correspond to the mass-sheddingfrequency for the observed systems and is simply a consequence of the,currently unknown, state of matter at high densities. Given our ignorance withregard to the true equation of state of matter above nuclear saturationdensities, we make minimal physical assumption and only demand causality in thecore. We then connect our causally-limited equation of state to a realisticmicrophysical crustal equation of state for densities below nuclear saturationdensity. This produces a limiting model that will give the lowest possiblemaximum frequency, which we compare to observational constraints on neutronstar masses and frequencies. We also compare our findings with the constraintson the tidal deformability obtained in the observations of the GW170817 event.We find that the lack of pulsars spinning faster than $f\approx 700$ Hz is notcompatible with our causal limited `minimal' equation of state, for which thebreakup frequency cannot be lower than $f_{\rm max}\approx 1200$ Hz. A lowfrequency cutoff, around $f\approx 800$ Hz could only be possible if we assumethat these systems do not contain neutron stars with masses above $M\approx 2M_\odot$. This would have to be due either to selection effects, or possibly toa phase transition in the interior of the neutron star.

Fundamental physics and the absence of sub-millisecond pulsars