Physics[Tetrads][l_] - represent the 1st null vector of the Newman-Penrose formalism
Physics[Tetrads][n_] - represent the 2nd null vector of the Newman-Penrose formalism, i.e. n_[mu] l_[mu] = 1
Physics[Tetrads][m_] - represent the 3rd null vector of the Newman-Penrose formalism, i.e. m_[mu] n_[mu] = 0, m_[mu] l_[mu] = 0
Physics[Tetrads][mb_] - represent the 4th null vector of the Newman-Penrose formalism, i.e. mb_ = conjugate(m_) and mb_[mu] m_[mu] = -1, mb_[mu] n_[mu] = 0, mb_[mu] l_[mu] = 0
Calling Sequence
l_[mu]
n_[mu]
m_[mu]
mb_[mu]
l_[a, matrix]
l_[keyword]
Parameters
_mu
-
the spacetime indices 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
_a_
a tetrad indices related to a local system of references, as names representing integer numbers the same way as the spacetime indices
keyword
optional, it can be definition, matrix, nonzero
Examples
withPhysics:withTetrads
_______________________________________________________
Setting lowercaselatin_ah letters to represent tetrad indices
Defined as tetrad tensors see ?Physics,tetrads, 𝔢a,μ , ηa,b , γa,b,c , λa,b,c
Defined as spacetime tensors representing the NP null vectors of the tetrad formalism see ?Physics,tetrads, lμ , nμ , mμ , m&conjugate0;μ
IsTetrad,NullTetrad,OrthonormalTetrad,PetrovType,SegreType,TransformTetrad,WeylScalars,e_,eta_,gamma_,l_,lambda_,m_,mb_,n_
Setupmathematicalnotation=true
mathematicalnotation=true
See Also
d_, D_, e_, eta_, g_, gamma_, IsTetrad, lambda_, NullTetrad, OrthonormalTetrad, Physics, Physics conventions, Physics examples, Physics Updates, Tensors - a complete guide, Mini-Course Computer Algebra for Physicists, Tetrads, TransformTetrad
References
Textbooks
Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.
Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C. Herlt, E. Exact Solutions of Einstein's Field Equations, Cambridge Monographs on Mathematical Physics, second edition. Cambridge University Press, 2003.
Compatibility
The Physics[Tetrads][l_], Physics[Tetrads][n_], Physics[Tetrads][m_] and Physics[Tetrads][mb_] commands were introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
The Physics[Tetrads][l_], Physics[Tetrads][n_], Physics[Tetrads][m_] and Physics[Tetrads][mb_] commands were updated in Maple 2017.
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