4.3 Neutron-Star Binaries4 Neutron-Star Initial Data4.1 Hydrostatic Equilibrium

4.2 Isolated Neutron Stars 

The simplest models of isolated neutron stars are static (i. e., nonrotating), spherically symmetric models that can be constructed, given a suitable equation of state, by solving the Oppenheimer-Volkoff (OV) equations [84]:

  eqnarray1510

for tex2html_wrap_inline3645, where R is the radius of the surface of the star. Here, r is an areal radius and m (r) is the mass inside radius r . Exterior to the surface of the star, the metric is the standard Schwarzschild metric as in Eq. (59Popup Equation) with tex2html_wrap_inline3655 . Interior to the surface of the star, the metric is

  equation1524

The boundary conditions are that m (0)=0, tex2html_wrap_inline3659 is some chosen constant tex2html_wrap_inline3661, and tex2html_wrap_inline3663 . The solutions of this equation form a one-parameter family, parameterized by tex2html_wrap_inline3661 which determines how relativistic the system is. A method for solving these equations in both the areal coordinate r and an isotropic radial coordinate tex2html_wrap_inline3501 can be found in Ref. [32Jump To The Next Citation Point In The Article].

More generally, isolated neutron stars will be rotating. If the neutron stars are uniformly rotating, then, for any given equation of state, the solutions form a two-parameter family. These models can be parameterized by their central density, which determines how relativistic they are, and by the amount of rotation. If the models are allowed to have differential rotation, then some rotation law must be chosen.

To construct a neutron-star model, the equations for a stationary solution of Einstein's equations outlined in Section  2.4 must be solved self-consistently with the equations for hydrostatic equilibrium of the matter outlined above in Section  4.1 . The equations that must be solved depend on the form of the metric chosen, and numerous formalisms and numerical schemes have been used. An incomplete list of references to work on constructing neutron-star models include [103, 22, 34, 32, 35, 33, 52, 62, 63, 43, 45, 44, 98, 21, 56, 16, 19]. Further review information on neutron-star models can be found in Refs. [97, 51, 50].



4.3 Neutron-Star Binaries4 Neutron-Star Initial Data4.1 Hydrostatic Equilibrium

image Initial Data for Numerical Relativity
Gregory B. Cook
http://www.livingreviews.org/lrr-2000-5
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