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

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

 > $\mathrm{with}\left(\mathrm{Physics}\right):$$\mathrm{with}\left(\mathrm{Tetrads}\right)$
 ${}\mathrm{_______________________________________________________}$
 $\mathrm{Setting}{}\mathrm{lowercaselatin_ah}{}\mathrm{letters to represent}{}\mathrm{tetrad}{}\mathrm{indices}$
 $\mathrm{Defined as tetrad tensors}{}\left(\mathrm{see ?Physics,tetrads}\right){},{}{𝔢}_{a,\mathrm{\mu }}{},{}{\mathrm{\eta }}_{a,b}{},{}{\mathrm{\gamma }}_{a,b,c}{},{}{\mathrm{\lambda }}_{a,b,c}$
 $\mathrm{Defined as spacetime tensors representing the NP null vectors of the tetrad formalism}{}\left(\mathrm{see ?Physics,tetrads}\right){},{}{l}_{\mathrm{\mu }}{},{}{n}_{\mathrm{\mu }}{},{}{m}_{\mathrm{\mu }}{},{}{\stackrel{&conjugate0;}{m}}_{\mathrm{\mu }}$
 ${}\mathrm{_______________________________________________________}$
 $\left[{\mathrm{IsTetrad}}{,}{\mathrm{NullTetrad}}{,}{\mathrm{OrthonormalTetrad}}{,}{\mathrm{PetrovType}}{,}{\mathrm{SegreType}}{,}{\mathrm{TransformTetrad}}{,}{\mathrm{e_}}{,}{\mathrm{eta_}}{,}{\mathrm{gamma_}}{,}{\mathrm{l_}}{,}{\mathrm{lambda_}}{,}{\mathrm{m_}}{,}{\mathrm{mb_}}{,}{\mathrm{n_}}\right]$ (1)
 > $\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$
 $\left[{\mathrm{mathematicalnotation}}{=}{\mathrm{true}}\right]$ (2)
 >