The matter is modeled as a perfect fluid because observations of pulsar glitches have shown that the departures from perfect fluid equilibrium due to the solid crust are of order . The temperature of a cold neutron star is assumed to be 0 K because its thermal energy (<<1MeV K) is much smaller than the Fermi energy of the interior (> 60 MeV). One can then use a zero-temperature (one-parameter) equation of state (EOS) to describe the matter:
where is the energy density and P is the pressure. At birth, a neutron star is differentially rotating, but as the neutron star cools, shear viscosity, resulting from neutrino diffusion, aided by convective and turbulent motions and possibly by the winding-up of magnetic field lines, enforces uniform rotation. At present, it is difficult to accurately compute the timescale in which uniform rotation is enforced, but it is estimated to be of the order of thousands of seconds [A3] .
Within roughly a year after its formation, the neutron star temperature becomes less than K, and its outer core becomes superfluid (See  and references therein.). Rotation causes the superfluid neutrons to form an array of quantized vortices, with an intervortex spacing of
where is the angular velocity of the star in . On scales much larger than the intervortex spacing, e.g. on the order of 1 cm, the fluid motions can be averaged and the rotation can be considered uniform .The error in computing the metric is of order
where R is a typical neutron star radius .
The above arguments show that the bulk properties of a rotating relativistic star can be modeled accurately by a uniformly rotating, zero-temperature perfect fluid.
|Rotating Stars in Relativity
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