Physics[Tetrads][e_] - represent and compute a tetrad (vierbein) and the corresponding null vectors of the Newman-Penrose formalism
Physics[Tetrads][eta_] - represent the (tetrad) metric of a local system of references
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Calling Sequence
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e_[a, mu]
e_[a, mu, keyword]
e_[keyword]
eta_[a, b]
eta_[a, b, keyword]
eta_[keyword]
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Parameters
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_mu
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a spacetime index related to a global system of references, these are names representing integer numbers between 0 and the spacetime dimension, they can also be the numbers themselves
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_a, b_
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the tetrad indices related to a local system of references, as names representing integer numbers the same way as the spacetime indices
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keyword
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optional, it can be definition, matrix, nonzero, and can be given alone or together with covariant or contravariant indices.
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Description
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The e_[a, mu] and eta[a, b] commands respectively represent the tetrad (also vierbein; by default, this is an orthonormal tetrad) and the tetrad metric, that is, the metric of the local frame - which by default is inertial, of Minkowski type. These two tensors are defined in terms of each other by .
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Both e_ and eta_ accept the keywords accepted by the other tensors of the Physics package, these are definition, matrix and nonzero, that can be given with or without indices. If given with indices, the corresponding output takes their character (covariant or contravariant) into account. In the case of e_, you can also use the keyword nullvectors, to see the null vectors corresponding to a given tetrad. Note anyway that these null vectors are available as commands of the Tetrads package; these are the l_, n_, m_ and mb_ commands.
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Examples
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In a flat space, the spacetime and tetrad metrics are the same, so the orthonormal tetrad is just the identity
In a curved spacetime, for instance, set a Local Rotational Symmetry metric metric:
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The default orthonormal tetrad is now
The following null vectors correspond to this tetrad:
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You can compute these null vectors directly since these are also part of the Tetrads package:
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You can query about the definition of any of these tensors in the same way you can now query any other tensor:
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Verify the definition of the tetrad given above
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See Also
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d_, D_, g_, gamma_, IsTetrad, l_, lambda_, m_, mb_, n_, NullTetrad, OrthonormalTetrad, Physics, Physics conventions, Physics examples, Physics Updates, Tensors - a complete guide, Mini-Course Computer Algebra for Physicists, Tetrads, TransformTetrad
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Compatibility
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The Physics[Tetrads][e_] and Physics[Tetrads][eta_] commands were introduced in Maple 2015.
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