represents the 1st null vector of the Newman-Penrose formalism - Maple Programming Help

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Physics[Tetrads][l_] - represents the 1st null vector of the Newman-Penrose formalism

Physics[Tetrads][n_] - represents the 2nd null vector of the Newman-Penrose formalism, i.e. n_[mu] l_[mu] = 1

Physics[Tetrads][m_] - represents the 3rd null vector of the Newman-Penrose formalism, i.e. m_[mu] n_[mu] = 0, m_[mu] l_[mu] = 0

Physics[Tetrads][mb_] - represents 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

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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: see ?Physics,tetrads, lμ, nμ, mμ, m&conjugate0;μ

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IsTetrad,NullTetrad,OrthonormalTetrad,PetrovType,SegreType,TransformTetrad,e_,eta_,gamma_,l_,lambda_,m_,mb_,n_

(1)

Setupmathematicalnotation=true

mathematicalnotation=true

(2)

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

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.