2.2 Geometry of Space-Time2 The Equilibrium Structure of 2 The Equilibrium Structure of

2.1 Assumptions

Although a relativistic star has a complicated structure (solid crust, magnetic field, possible superfluid interior, etc.), its bulk properties can be computed with reasonable accuracy by making several simplifying assumptions.

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 tex2html_wrap_inline1957 [1Jump To The Next Citation Point In The Article]. The temperature of a cold neutron star is assumed to be 0 K because its thermal energy (<<1MeV tex2html_wrap_inline1961 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:

equation15

where tex2html_wrap_inline1965 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 [A3Jump To The Next Amendment] [2Jump To The Next Citation Point In The Article].

Within roughly a year after its formation, the neutron star temperature becomes less than tex2html_wrap_inline1969 K, and its outer core becomes superfluid (See [3] and references therein.). Rotation causes the superfluid neutrons to form an array of quantized vortices, with an intervortex spacing of

equation19

where tex2html_wrap_inline1971 is the angular velocity of the star in tex2html_wrap_inline1973 . 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 [4].The error in computing the metric is of order

equation27

where R is a typical neutron star radius [1Jump To The Next Citation Point In The Article].

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.



2.2 Geometry of Space-Time2 The Equilibrium Structure of 2 The Equilibrium Structure of

image Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-1998-8
© Max-Planck-Gesellschaft. ISSN 1433-8351
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