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

Abstract

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_sph^max, we find P[ms] > 0.282 + 0.196 ( M_sph^max/M_odot-1.442). The limit does not assume that the EOS agrees with a known low-density form for ordinary matter, but if one adds that assumption, the minimum period is raised by a few percent. Thus the current minimum period of uniformly rotating stars, set by causality, is 0.28ms (0.29ms for stars with normal crust). 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, epsilon_m. We recompute it, obtaining a slightly revised value, M_rot^max \sim 6.1( 2 * 10^14 g/cm^3 epsilon_m )^1/2 M_odot.