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Question: Showing Weyl tensor is equal to zero in 3D

Question:Showing Weyl tensor is equal to zero in 3D

guru kido 60 Maple
physics
May 09 2019
0


 

> 

with(Physics)
> 

Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)
> 

Setup(dimension = 3, coordinates = (X = [x1, x2, x3]), metric = 2*F6(X)*dx2*dx3+2*F5(X)*dx1*dx3+2*F4(X)*dx1*dx2+F1(X)*dx1^2+F2(X)*dx2^2+F3(X)*dx3^2)

`* Partial match of 'coordinates' against keyword 'coordinatesystems'`

  

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (x1, x2, x3)}

  

`Systems of spacetime Coordinates are: `*{X = (x1, x2, x3)}

  

[coordinatesystems = {X}, dimension = 3, metric = {(1, 1) = F1(X), (1, 2) = F4(X), (1, 3) = F5(X), (2, 2) = F2(X), (2, 3) = F6(X), (3, 3) = F3(X)}]

 (2)
> 

g_[]

Physics:-g_[mu, nu] = Matrix(%id = 18446746167581484926)

 (3)
> 

Weyl[alpha, beta, mu, nu, nonzero]

`[Length of output exceeds limit of 1000000]`

 (4)

Weyl tensor is identically equal to zero in 3D and I have tried to show this by inputting an arbitrary metric and calculating components of Weyl tensor. Thus this answer should give me the empty set but I am not getting that, thanks in advance.

CODE:

with(Physics):

Setup(mathematicalnotation = true)

Setup(dimension = 3, coordinates = (X = [x1, x2, x3]), metric = 2*F6(X)*dx2*dx3+2*F5(X)*dx1*dx3+2*F4(X)*dx1*dx2+F1(X)*(dx1^2)+F2(X)*(dx2^2)+F3(X)*(dx3^2))


g_[]

Weyl[alpha, beta, mu, nu, nonzero]

 

Download Weyltensor0in3d.mw
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