Upper Limits Set by Causality on the Rotation and Mass of Uniformly Rotating Relativistic Stars

Causality alone suffices to set a lower bound on the period of rotation of relativistic stars as a function of their maximum observed mass. That is, by assuming a one-parameter equation of state (EOS) that satisfies v sound < c and that allows stars with masses as large as the largest observed neutron star mass, M , we find P (ms)>0.282+0.196( M / M -1.442). The limit does not assume that the EOS agrees with a known low-density form for ordinary matter, and if one adds that assumption, the minimum period is raised by a few percent: for a match at n = 0.1 fm -3 , we find P (ms)>0.295 + 0.203( M / M -1.442). The minimizing EOS yields models with a maximally soft exterior supported by a maximally stiff core. An analogous upper limit set by causality on the maximum mass of rotating neutron stars requires a low-density match, and the limit depends on the matching density, m . We recompute it, obtaining a slightly revised value, M ≃6.1(2 × 10 14 g cm -3 / m ) 1/2 M ☉ .