The code XNS solves for the axisymmetric equilibrium configuration of differentially rotating Neutron Stars with toroidal magnetic field, using the XCFC approximation for the metric, in spherical coordinates. The code is based on the metric module and routines developed for the GR-MHD code X-ECHO .
You can download an older version of the code XNS here !
And an older Guide!
There are several other codes published in the years (RNS, RotStar, etc....) you might want to check.
However, solutions, even for rapid rotators close to the mass shedding limit, show that the difference
between conformally flat metric CFC/XCFC, and the more appropriate quasi-isotropic coordinates is
order of 0.1% (larger differences are expected for strongly distorted cases of disk-like configurations), so in principle one would expect the CFC/XCFC limit to provide a reasonably good approximation of the
correct solution for Neutron Stars. There are some computational benefits in using XCFC over quasi-isotropic coordinates, and as an Astrophysicist I am looking more toward a solution that is physically acceptable than one that is mathematically correct.
These are some comparisons with the code RNS, for a uniform rotator close to mass shedding limit. You can see that the errors are ~0.1% or smaller. On the left is a comparison of the polar, and equatorial densities: the solid lines are from RNS and the dashed lines (can you see them?) from XNS. On the right is a comparison of the errors in the metric terms. All the lines that you see represent various metric terms (see the Guide for explanation). They are all < 0.1%, the dash dotted line is a measure of how far from conformally-flat the RNS result is. That indicates the quality of the CFC/XCFC approximation.
Here is instead a differentially rotating magnetized solution.
There are still a few things that can/must be improved: