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SageMath notebooks associated to the Black Hole Lectures (https://luth.obspm.fr/~luthier/gourgoulhon/bh16)
Project: BHLectures
Views: 20107Kernel: Sage 6.9
Light cone in Minkowski spacetime
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4-dimensional differentiable manifold M
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Vector field l on the 4-dimensional differentiable manifold M
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Levi-Civita connection nabla_g associated with the Lorentzian metric g on the 4-dimensional differentiable manifold M
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Tensor field nabla_g(l) of type (1,1) on the 4-dimensional differentiable manifold M
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Vector field on the 4-dimensional differentiable manifold M
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Let us check that is a null vector:
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and that it obeys :
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1-form lf on the 4-dimensional differentiable manifold M
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1-form kf on the 4-dimensional differentiable manifold M
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Tensor field q of type (0,2) on the 4-dimensional differentiable manifold M
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Field of symmetric bilinear forms q on the 4-dimensional differentiable manifold M
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Check of the inverse coordinate transformation:
t == t
r == r
th == arctan2(r*sin(th), r*cos(th))
ph == arctan2(r*sin(ph)*sin(th), r*cos(ph)*sin(th))
t == t
x == x
y == y
z == z
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Tensor field of type (2,0) on the 4-dimensional differentiable manifold M
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Scalar field on the 4-dimensional differentiable manifold M
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