Maximum redshift and minimum rotation period of neutron stars

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The lower bound on the period of uniform rotation of neutron stars (NS) with causal equation of state (EOS), P min, is shown to be determined, with a high precision, by the upper bound on the surface redshift of static neutron star models, z max. We obtain zₘax=0.851, which turns out to be about 5% lower than upper bound obtained by Lindblom (1984). Using then the empirical formula for the maximum rotation frequency of uniform rotation of neutron star models with realistic causal EOS, derived by Lasota et al. (1996), we establish an approximate relation between zₘax and Pₘin, in which Pₘin is proportional to the maximum mass of static NS, Mₛ max. In this way we reproduce, within 2%, the exact formula of Koranda et al. (1997) based on extensive exact numerical calculations. Replacing Mₛᵐax by the maximum measured NS mass, 1.442 Mₛun, we get a lower bound Pₘin = 0.288 ms.