Assumptions

2.1 Assumptions

A relativistic star can have a complicated structure (such as a solid crust, magnetic field, possible superfluid interior, possible quark core, etc.). Still, its bulk properties can be computed with reasonable accuracy by making several simplifying assumptions.

The matter can be modeled to be a perfect fluid because observations of pulsar glitches have shown that the departures from a perfect fluid equilibrium (due to the presence of a solid crust) are of order 10^–5 (see [112 ]). The temperature of a cold neutron star does not affect its bulk properties and can be assumed to be 0 K, because its thermal energy ( $10 ≪ 1 MeV ∼ 10 K$ ) is much smaller than Fermi energies of the interior ( $>$ 60 MeV). One can then use a zero-temperature, barotropic equation of state (EOS) to describe the matter:

where $𝜀$ is the energy density and $P$ is the pressure. At birth, a neutron star is expected to be rotating differentially, but as the neutron star cools, several mechanisms can act to enforce uniform rotation. Kinematical shear viscosity is acting against differential rotation on a timescale that has been estimated to be [101

, 102 , 78 ]

where $ρ$ , $T$ and $R$ are the central density, temperature, and radius of the star. It has also been suggested that convective and turbulent motions may enforce uniform rotation on a timescale of the order of days [153 ]. In recent work, Shapiro [266 ] suggests that magnetic braking of differential rotation by Alfvén waves could be the most effective damping mechanism, acting on short timescales of the order of minutes.

Within roughly a year after its formation, the temperature of a neutron star becomes less than 10⁹ K and its outer core is expected to become superfluid (see [226 ] and references therein). Rotation causes superfluid neutrons to form an array of quantized vortices, with an intervortex spacing of

where $Ω2$ is the angular velocity of the star in 10² s^–1. 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 to be uniform [284 ]. With such an assumption, the error in computing the metric is of order

assuming $R ∼ 10 km$ to be a typical neutron star radius.

The above arguments show that the bulk properties of an isolated rotating relativistic star can be modeled accurately by a uniformly rotating, zero-temperature perfect fluid. Effects of differential rotation and of finite temperature need only be considered during the first year (or less) after the formation of a relativistic star.