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Example 1.
First create manifold with coordinates .
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Define a spacetime metric on with signature .
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| (2.2) |
Define an orthonormal tetrad F on with respect to the metric . Verify using the command GRQuery.
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| (2.3) |
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Use the orthonormal tetrad F to construct a null tetrad NT.
| (2.5) |
Verify this result using the command GRQuery.
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It is a simple matter to check directly, using the TensorInnerProduct command, that NT is a null tetrad,
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Example 2.
We use spinors to create a null tetrad. First create a vector bundle with base coordinates and fiber coordinates .
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Define a spacetime metric on with signature .
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| (2.8) |
Define an orthonormal frame on with respect to the metric .
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| (2.9) |
Compute the solder form defined by the orthonormal frame .
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| (2.10) |
Define a pair of rank 1 spinors and . Check that their spinor inner product is 1. Construct the corresponding null tetrad, .
| (2.11) |
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| (2.12) |
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| (2.14) |
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Example 3.
Convert the null tetrad constructed in Example 2 to an orthonormal tetrad .
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| (2.15) |
Check the result.
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