This is some matterial that could be a helpfull companion to the paper,
"An all-purpose metric for the exterior of any kind of rotating neutron star", by G. Pappas and T. A. Apostolatos.

metric functions for the spacetimes used

reading the numerical data and calculating everything in Weyl-Papapetrou coordinates

calculating the specific two-soliton metric

In[1226]:=

Print["================ the two-soliton parameters =================="] ;

Print["=================== CTCs and SLSs ====================="] ;

Show[plot2SLS_modIn, plot2CTC_modIn] ;

================ the two-soliton parameters ==================

b= -0.380625    k= -13.5463

d = 12.9637

κ = 0.970415 +

κ = 0. + 7.13535  -

Case IIa

Case IIa

=================== CTCs and SLSs =====================

[Graphics:HTMLFiles/index_201.gif]

Out[1231]=

{28.516 Second, Null}

[Graphics:HTMLFiles/index_203.gif]

Out[1232]=

{121.109 Second, Null}

[Graphics:HTMLFiles/index_205.gif]

calculating the corresponding Manko et al. spacetimes

In[1118]:=

Print["Manko et al."] ;

Print[b = , Val_3, ,   b = , Val_4] ; - +

Off[Graphics :: "gptn"] ;

Manko et al.

[Graphics:HTMLFiles/index_214.gif]

b = -0.601542 ,   b = 2.94721 - +

comparing the metric functions between the numerical spacetime and the two-soliton, the Hartle-Thorne and the two corresponding Manko et al. solutions

In[1260]:=

Show[GraphicsArray[{{plot1, plot2}, {ΔRcircPlot, ΔgzzEqPlot}, {ΔgttAxPlot}}]] ;

[Graphics:HTMLFiles/index_257.gif]

comparing the ISCO for the two-soliton

In[1140]:=

Print["=============== calculating the ISCO =================="] ;

Print[Co - rotating] ;

Print[Counter - rotating] ;

=============== calculating the ISCO ==================

Co - rotating

{ρ→11.3791, Ep→0.942902, Lp→7.04662}

Counter - rotating

{ρ→18.4127, Ep→0.964045, Lp→ -8.98615}

ΔR ISCO (------------) = 2.09175% for the counter-rotating R ISCO

ΔR ISCO (------------) = 27.6109% for the co-rotating R ISCO

j = 0.698847

comparing the frequencies and ΔOverscript[Ε, ~]

In[1196]:=

~ Print[=============== comparing the frequencies and Δ E ==================] ;

Print[Ω] ;

~ =============== comparing the frequencies and Δ E ==================

Out[1197]=

{24.39 Second, Null}

-1 Ω = 0.0155998 km for the counter-rotating ISCO

-1 Ω = 0.0297306 km for the co-rotating ISCO

u = 0.396583 for the co-rotating ISCO

4.67665 kHz

8.91295 kHz

0.00134352 Second

0.00070495 Second

Ω

[Graphics:HTMLFiles/index_297.gif]

Out[1200]=

{8.531 Second, Null}

[Graphics:HTMLFiles/index_299.gif]

Out[1201]=

{209.453 Second, Null}

[Graphics:HTMLFiles/index_301.gif]

Out[1202]=

{3.438 Second, Null}

[Graphics:HTMLFiles/index_303.gif]

Out[1203]=

{85.765 Second, Null}

Ω , Ω ρ z

Out[1204]=

{11.297 Second, Null}

[Graphics:HTMLFiles/index_307.gif]

Out[1205]=

{27.297 Second, Null}

[Graphics:HTMLFiles/index_309.gif]

Out[1206]=

{16.343 Second, Null}

In[1207]:=

ModelTypeTab//MatrixForm

DRiscoTabP//MatrixForm

DRiscoTabM//MatrixForm

ModelTypeTab3 = ModelTypeTab ;

DRiscoTabP3 = DRiscoTabP ;

DRiscoTabM3 = DRiscoTabM ;

Out[1207]//MatrixForm=

Out[1208]//MatrixForm=

( {{0.698847, -3.5661, -5.20138, 0.276109, Null, Null, Null, Null}} )

Out[1209]//MatrixForm=

( {{-0.698847, -3.5661, 5.20138, 0.0209175, Null, Null, Null, Null}} )

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