2.2 Geometry of spacetime2 The Equilibrium Structure of 2 The Equilibrium Structure of

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 tex2html_wrap_inline3676 (see [112Jump To The Next Citation Point In The Article]). 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 (tex2html_wrap_inline3678) is much smaller than Fermi energies of the interior (tex2html_wrap_inline3680). One can then use a zero-temperature, barotropic equation of state (EOS) to describe the matter:

equation25

where tex2html_wrap_inline3682 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 [101Jump To The Next Citation Point In The Article, 102, 78]

equation28

where tex2html_wrap_inline3686, 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 [267] 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 tex2html_wrap_inline3692 and its outer core is expected to become superfluid (see [227] and references therein). Rotation causes superfluid neutrons to form an array of quantized vortices, with an intervortex spacing of

equation45

where tex2html_wrap_inline3694 is the angular velocity of the star in tex2html_wrap_inline3696 . 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 [285]. With such an assumption, the error in computing the metric is of order

equation55

assuming tex2html_wrap_inline3698 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.



2.2 Geometry of spacetime2 The Equilibrium Structure of 2 The Equilibrium Structure of

image Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-2003-3
© Max-Planck-Gesellschaft. ISSN 1433-8351
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