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Question: Non zero Christoffel display

Question:Non zero Christoffel display

albivaldmaple 20 Maple 2016
tensor physics christoffel
March 08 2023
2

Hello everyone

I create a curved space ( with Physics) and create a metric tensor of 

a sphere . I see some Christoffel correcly . Is it possible to visualize all non zero Christoffel in one shot ?

Thank's a lot

Best Regards

restart; with(Physics)

Physics:-Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)

Physics:-Setup(spacetimeindices, dimension = 2, signature = "++")

[dimension = 2, signature = `+ +`, spacetimeindices = greek]

 (2)

Physics:-Coordinates(X)

{X}

 (3)

ds2 := Physics:-`^`(dx1, 2)+Physics:-`*`(Physics:-`^`(sin(x1), 2), Physics:-`^`(dx2, 2))

dx1^2+sin(x1)^2*dx2^2

 (4)

NULL

Physics:-Setup(metric = ds2)

[metric = {(1, 1) = 1, (2, 2) = sin(x1)^2}]

 (5)

NULL

NULL

g_[]

g[mu, nu] = (Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 2) = sin(x1)^2}, storage = triangular[upper], shape = [symmetric]))

 (6)

Physics:-Christoffel[`~k`, i, j]

Physics:-Christoffel[`~k`, i, j]

 (7)

Physics:-Christoffel[`~1`, 2, 2]

-sin(x1)*cos(x1)

 (8)

Physics:-Christoffel[`~2`, 1, 2]

cos(x1)/sin(x1)

 (9)

Physics:-Christoffel[`~1`, 1, 1]

0

 (10)

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