CoCalc -- Frolov_Novikov

SageMath notebooks associated to the Black Hole Lectures (https://luth.obspm.fr/~luthier/gourgoulhon/bh16)

Path: BHLectures/sage / Frolov_Novikov_conformal.ipynb

Views: ²⁰¹⁰⁷

Kernel: SageMath 7.4.beta6

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%display latex

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var('u v')

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def W(x):
    if x < -1:
        return RDF(0)
    return RDF(lambert_w(RDF(x)/RDF(e))+1)

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plot(W, (x,-2,5), aspect_ratio=1)

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def h(u,v):
    return sinh(tan(u))*sinh(tan(v))-1

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a = 0.99*pi/2

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implicit_plot(h, (u,-a,a), (v,-a,a), plot_points=400, fill=True, fillcolor='yellow')

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def g(u,v):
    return 4*W(-sinh(tan(u))*sinh(tan(v)))^2 * cos(u)^2 * cos(v)^2

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graph = plot3d(g, (u,-a,a), (v,-a,a), plot_points=200)

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graph += plot3d(lambda u,v: 0.001, (u,-a,a), (v,-a,a), color='yellow')

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show(graph.rotate((0,0,1), pi/2), viewer='tachyon', view_point=(-3,3,2))

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graph

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