Working with tetrads and the spin connection

asked 2021-04-30 16:35:30 +0100

JackHughes14
35 ●1 ●5

Using sagemanifolds, is there any way to work within the tetrad formalism and calculate the spin connection coefficients for some specified spacetime manifold and choice of vierbein?

answered 2021-05-01 15:14:02 +0100

eric_g
8424 ●10 ●62 ●166 https://luth.obspm.fr/...

updated 2021-05-01 15:24:09 +0100

Spin connections are not implemented yet. However, note that generic tetrads are implemented and that the connection coefficients of the Levi-Civita connection can be expressed in any tetrad, see the methods coef() and connection_form() of affine connections. So you can introduce a null tetrad by hand (cf. VectorFrame) and compute the spin coefficients by means of the above methods.

If you are interested in implementing null tetrads and spin coefficients in SageMath, you are very welcome! Please visit this page.

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Hei... It's many years... I was actually trying to find the tetrads but it's not clear to me how you suggested. Can you help? I am trying to get the tetrads defined in equations - 4 of the paper : arXiv:1004.5487v2 [gr-qc] 30 Dec 2010

Rousan ( 2024-03-21 09:59:14 +0100 )edit

Here is an example notebook implementing the computation of Newman-Penrose and GHP spin coefficients.

eric_g ( 2024-07-02 00:49:53 +0100 )edit

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