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%%  definitions for paper
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 %:: \textheight27.5cm
 %:: \hoffset-1cm
 %:: \voffset-2cm
 %:: \pagestyle{empty}





\eqnobysec        % equations numbered by section                   %:skip:
                                                                    %:: \mbox{}\newpage


\DeclareOption{datedpages}{%                                        %:skip:
\renewcommand{\date}[1]{%                                           %:skip:
\vspace*{2ex}{\textsf{\small #1}}%                                  %:skip:
\def\thepage{{\textsf{\small #1}}\qquad\arabic{page}}}              %:skip:
}                                                                   %:skip:

  %\def\ps@headings{\let\@oddfoot\@empty
  %      \let\@evenfoot\@empty
  %      \def\@evenhead{\thepage\hfil\itshape\rightmark}%
  %      \def\@oddhead{{\itshape\leftmark}\hfil\thepage}%
  %      \let\@mkboth\markboth
  %      \let\sectionmark\@gobble
  %      \let\subsectionmark\@gobble}



%%% text, punctation

  \newcommand{\defterm}[1]{\textit{#1}}                             %:text:
  \newcommand{\vague}[1]{`#1'}                                      %:text:

  \newcommand{\spcpnct}{\;}                              % space before punctation in equation
  \newcommand{\spce}{\spcpnct\:}                         % space at the end of equation (for alignment with punctation)
  \newcommand{\period}{{\mbox{\spcpnct.}\relax}}         % period at the end of equation
  \newcommand{\commae}{{\mbox{\spcpnct,}\relax}}         % comma at the end of equation
  \newcommand{\comma}{{\mbox{\spcpnct,\quad}\relax}}     % comma between equations
  \newcommand{\spcm}{{\mspace{14.5mu}}}                  % space with width of minus
  \newcommand{\nquad}{{\mspace{-20mu}}}                  % negative quad 
  \newcommand{\textdash}{{\text{-}}}                     % text dash for equations


%%% miscellaneous objects

  \newcommand{\naturaln}{{\mathbb{N}}}
  \newcommand{\integern}{{\mathbb{Z}}}
  \newcommand{\realn}{{\mathbb{R}}}
  \newcommand{\complexn}{{\mathbb{C}}}
  \newcommand{\abs}[1]{\left\lvert#1\right\rvert}
  \newcommand{\bigabs}[1]{\bigl\lvert#1\bigr\rvert}
  \newcommand{\lteq}{\approx}
  \DeclareMathOperator{\csch}{csch}
  \DeclareMathOperator{\sech}{sech}
  \DeclareMathOperator{\sign}{sign}
  \DeclareMathOperator{\re}{Re}
  \DeclareMathOperator{\im}{Im}
  \newcommand{\OO}{\mathcal{O}}

  \newcommand{\tht}{\vartheta}
  \newcommand{\ph}{\varphi}
  \newcommand{\eps}{\varepsilon}
  \newcommand{\kap}{\varkappa}
  \newcommand{\omicron}{{\mathit{o}}}


%%% labels

  %\newcommand{\onscri}{{\scriptscriptstyle{\infty}}}          % on $\scri$
  \newcommand{\EM}{{\scriptscriptstyle\mathrm{EM}}}           % electromagnetic
  \newcommand{\auxT}{{\mathrm{a}}}         % (conformal) auxiliary tetrad
  \newcommand{\intT}{{\mathrm{i}}}         % interpretation tetrad
  \newcommand{\refT}{{\mathrm{o}}}         % reference tetrad
  \newcommand{\spcT}{{\mathrm{s}}}         % scaled interpretation tetrad
  \newcommand{\bstT}{{\mathrm{b}}}         % boosted tetrad

  \newcommand{\PND}[1]{\tens{k}_{#1}}      % principal null direction                 %:ex:   \PND{1}
  \newcommand{\atbox}[1]{{\makebox[15pt][c]{$#1$}}}   % algebraic type                %:ex:   \atbox{iio^2}

                                                                                %:: \hfill
                                                                                %:page:


%%% tensors

  \newcommand{\tens}[1]{{\boldsymbol{\mathbf{#1}}}}     % tensor wrapper
  
  \newcommand{\spr}{\mathbin{\boldsymbol{\cdot}}}       % scalar product
  \newcommand{\ctr}{\cdot}                              % contraction
  \newcommand{\stp}{\mathbin{\scriptstyle{\vee}}}       % symetrical product

  %\newcommand{\cv}[1]{{\frac{\partial}{\partial #1}}}  % coordinate frame vectors
  %\newcommand{\cvil}[1]{{{\partial}/{\partial #1}}}    % inline coordinate frame vectors
  \newcommand{\cv}[1]{{\tens{\partial}_{#1}}}           % coordinate frame vectors
  \newcommand{\cvil}[1]{{\tens{\partial}_{#1}}}         % inline coordinate frame vectors







%%% physical geometry

  \newcommand{\mfld}{{\mathcal{M}}}        % physical manifold
  \newcommand{\mtrc}{\tens{g}}             % physical metric
  %\newcommand{\mtrc}{{\boldsymbol{g}}}    % physical metric
  \newcommand{\norm}{{\tens{n}}}           % physical normal to scri
  \newcommand{\nsgn}{\sigma}               % character of normal vector ($\nsgn=-1,0,+1$)

  
  \newcommand{\grad}{{\mathbf{d}}}         % gradient
  \newcommand{\lied}{{\mathcal{L}}}        % Lie derivative
  \newcommand{\covd}{\nabla}               % physical covariant derivative
  \newcommand{\dalamb}{\square}            % wave operator

  \newcommand{\RT}{\tens{R}}               % physical Riemann tensor
  \newcommand{\Ric}{\tens{Ric}}            % physical Ricci tensor
  \newcommand{\scR}{R}                     % physical scalar curvature
  \newcommand{\WT}{\tens{C}}               % physical Weyl tensor
  \newcommand{\WTSR}{\tens{\Psi}}          % physical Weyl tensor r-spinor
  \newcommand{\WTSL}{\bar\WTSR}             % physical Weyl tensor l-spinor
  \newcommand{\WTP}[2]{\Psi^{#1}_{#2}}     % physical Weyl tensor tetrad components   %:ex:   \WTP{\intT}{4}
  \newcommand{\RicciP}[2]{\Phi^{#1}_{#2}}  % physical Ricci tensor tetrad components  %:ex:   \RicciP{\refT}{01}

  \newcommand{\TEM}{\tens{T}}              % tensor of energy-momentum
  \newcommand{\scale}{\ell}                % typical scale


%%% conformal geometry

  \newcommand{\cmfld}{{\tilde\mfld}}       % conformal manifold
  \newcommand{\scri}{{\mathcal{I}}}        % scri
  \newcommand{\om}{\Omega}                 % conformal factor
  \newcommand{\cmtrc}{{\tilde{\mtrc}}}     % conformal metric
  \newcommand{\scricmtrc}{{{}^\scri\cmtrc}}% conformal metric on scri
  \newcommand{\cnorm}{{\tilde{\norm}}}     % conformal normal to scri
  \newcommand{\clapse}{{\tilde{N}}}        % conformal lapse
  
  \newcommand{\ccovd}{{\tilde\covd}}       % conformal covariant derivative
  \newcommand{\covddif}{\tens{\gamma}}     % difference of covariant derivatives
  \newcommand{\cdalamb}{{\tilde\dalamb}}   % wave operator
  
  \newcommand{\cRT}{{\tilde\RT}}           % conformal Riemann tensor
  \newcommand{\cRic}{{\tilde\Ric}}         % conformal Ricci tensor
  \newcommand{\cscR}{{\tilde\scR}}         % conformal scalar curvature
  \newcommand{\cWT}{{\tilde{\WT}}}         % conformal Weyl tensor
  \newcommand{\cRicciP}[2]{{\tilde\Phi}^{#1}_{#2}}  % conformal Ricci tensor tetrad components  %:ex:   \cRicciP{\refT}{01}


  


                                                                                %:: \hfill
                                                                                %:page:



%%% spinors

  \newcommand{\SX}{\scriptscriptstyle}      % $\verb|\SX|$ - spinor index                     %:ex:   \SRe_{\SX AB}
  \newcommand{\SC}[1]{\bar{#1}}             % $\verb|\SC|$ - spinor index conjugation         %:ex:   \SLi^{\SX\SC A}
  \newcommand{\SRspc}{{\mathbf{S}}}         % r-spinor space
  \newcommand{\SLspc}{{\bar{\mathbf{S}}}}   % l-spinor space
  
  \newcommand{\SRid}{\tens{\delta}}         % r-spinor identity
  \newcommand{\SLid}{\bar\SRid}             % l-spinor identity
  \newcommand{\SRe}{\tens{\epsilon}}        % r-spinor skew-metric
  \newcommand{\SLe}{\bar\SRe}               % l-spinor skew-metric
  \newcommand{\Ssf}{{\tens{\sigma}}}                                     % soldering form
  
  \newcommand{\SRDe}[2]{\SRe_{\SX #1#2}}                        % r-spinor skew-metric              %:ex:   \SRDe AB
  \newcommand{\SRUe}[2]{\SRe^{\SX #1#2}}                        % r-spinor inverse skew-metric      %:ex:   \SRUe AB
  \newcommand{\SLDe}[2]{\SLe_{\SX\SC{#1}\SC{#2}}}               % l-spinor skew-metric              %:ex:   \SLDe AB
  \newcommand{\SLUe}[2]{\SLe^{\SX\SC{#1}\SC{#2}}}               % l-spinor inverse skew-metric      %:ex:   \SLUe AB
  \newcommand{\SUsf}[3]{{\Ssf^{#1}\!{}_{\SX #2\SC{#3}}}}                 % soldering form                    %:ex:   \SUsf aAA
  \newcommand{\SDsf}[3]{{\Ssf_{#1}\mspace{-2mu}{}^{\SX #2\SC{#3}}}}      % soldering form                    %:ex:   \SDsf aAA


%%% field of spin s
  
  \newcommand{\field}{\tens{\Upsilon}}     % field of spin s
  \newcommand{\fieldP}[2]{\Upsilon^{#1}_{#2}} % filed components              %:ex:  \fieldP{\refT}{n}
  \newcommand{\bfieldP}[2]{{\bar\Upsilon}^{#1}_{#2}} % filed components       %:ex:  \bfieldP{\refT}{n}



%%% EM field
  

  \newcommand{\EMF}{\tens{F}}              % EM tensor
  \newcommand{\EME}{\tens{E}}              % eletric intensity
  \newcommand{\EMB}{\tens{B}}              % magnetic induction
  \newcommand{\EMu}{u}                     % density of EM energy
  \newcommand{\EMS}{\tens{S}}              % Poynting vector
  \newcommand{\EMJ}{\tens{J}}              % EM current
  \newcommand{\EMSR}{\tens{\Phi}}          % EM r-spinor
  \newcommand{\EMSL}{\bar\EMSR}             % EM l-spinor
  \newcommand{\EMP}[2]{\Phi^{#1}_{#2}}     % EM tetrad components              %:ex:  \EMP{\refT}{n}

%%% geodesics

  \newcommand{\geod}{z}                    % physical geodesic
  \newcommand{\afp}{\eta}                  % physical affine parameter
  \newcommand{\iafp}{\eps}                 % inverse physical affine parameter
  \newcommand{\mom}{{\tens{p}}}            % 4-momentum
  
  \newcommand{\cgeod}{\tilde{\geod}}       % geodesic
  \newcommand{\cafp}{\tilde{\afp}}         % affine parameter
  
  \newcommand{\EPS}{\epsilon}              % orientation of geodesic ($\EPS=\pm1$)
  \newcommand{\PSI}{\psi}                  % direction of geodesic
  \newcommand{\THT}{\theta}                % direction of geodesic
  \newcommand{\PHI}{\phi}                  % direction of geodesic
  \newcommand{\R}{R}                       % direction of geodesic ($\R\in\complexn$)
  \newcommand{\RHO}{\rho}                  % direction of geodesic

  \newcommand{\intTphi}{\phi}                % parametrization of int. tetrad
  \newcommand{\intTL}{L}                     % parametrization of int. tetrad
  \newcommand{\bstTL}{{\tilde L}}            % parametrization of rescaled int. tetrad
  \newcommand{\THTS}{{\THT_\spcT}}           % parametrization of alg. spec. tetrad
  
  \newcommand{\ant}{_{\mathfrak{a}}}         % antipodal direction       %:ex: \R\ant
  \newcommand{\mir}{_{\mathfrak{m}}}         % mirrored direction        %:ex: \R\mir




                                                                                %:: \hfill
                                                                                %:page:

%%% tetrads   

  
                                                                                %:: \begin{minipage}[t]{2.5in}

  %%% general tetrad
  \newcommand{\kG}{{\tens{k}}}
  \newcommand{\lG}{{\tens{l}}}
  \newcommand{\mG}{{\tens{m}}}
  \newcommand{\bG}{{\bar{\tens{m}}}}

  \newcommand{\tG}{{\tens{t}}}
  \newcommand{\qG}{{\tens{q}}}
  \newcommand{\rG}{{\tens{r}}}
  \newcommand{\sG}{{\tens{s}}}

                                                                                %:: \vspace{1.5mm}


  %%% interpretation tetrad
  \newcommand{\kI}{\kG_\intT}
  \newcommand{\lI}{\lG_\intT}
  \newcommand{\mI}{\mG_\intT}
  \newcommand{\bI}{\bG_\intT}

  \newcommand{\tI}{\tG_\intT}
  \newcommand{\qI}{\qG_\intT}
  \newcommand{\rI}{\rG_\intT}
  \newcommand{\sI}{\sG_\intT}

                                                                                %:: \vspace{1.5mm}

  %%% scaled int. tetrad
  \newcommand{\kB}{\kG_\bstT}
  \newcommand{\lB}{\lG_\bstT}
  \newcommand{\mB}{\mG_\bstT}
  \newcommand{\bB}{\bG_\bstT}

  \newcommand{\tB}{\tG_\bstT}
  \newcommand{\qB}{\qG_\bstT}
  \newcommand{\rB}{\rG_\bstT}
  \newcommand{\sB}{\sG_\bstT}

  

  %%% reference tetrad
  \newcommand{\kO}{\kG_\refT}
  \newcommand{\lO}{\lG_\refT}
  \newcommand{\mO}{\mG_\refT}
  \newcommand{\bO}{\bG_\refT}

  \newcommand{\tO}{\tG_\refT}
  \newcommand{\qO}{\qG_\refT}
  \newcommand{\rO}{\rG_\refT}
  \newcommand{\sO}{\sG_\refT}

                                                                               %:: \vspace{30pt}


  %%% r-spinor frame
  \newcommand{\SRi}{\tens{\iota}}           
  \newcommand{\SRo}{\tens{\omicron}}        



                                                                                %:: \end{minipage}
                                                                                %:: \begin{minipage}[t]{2.5in}


  %%% conformal general tetrad
  \newcommand{\kC}{{\tilde{\tens{k}}}}
  \newcommand{\lC}{{\tilde{\tens{l}}}}
  \newcommand{\mC}{{\tilde{\tens{m}}}}
  \newcommand{\bC}{{\bar{\tilde{\tens{m}}}}}

  \newcommand{\tC}{{\tilde{\tens{t}}}}
  \newcommand{\qC}{{\tilde{\tens{q}}}}
  \newcommand{\rC}{{\tilde{\tens{r}}}}
  \newcommand{\sC}{{\tilde{\tens{s}}}}



  %%% conf. parallelly transp. tetrad
  \newcommand{\kP}{\kC_\auxT}
  \newcommand{\lP}{\lC_\auxT}
  \newcommand{\mP}{\mC_\auxT}
  \newcommand{\bP}{\bC_\auxT}

  \newcommand{\tP}{\tC_\auxT}
  \newcommand{\qP}{\qC_\auxT}
  \newcommand{\rP}{\rC_\auxT}
  \newcommand{\sP}{\sC_\auxT}


  %%% auxiliary tetrad
  \newcommand{\kA}{\kG_\auxT}
  \newcommand{\lA}{\lG_\auxT}
  \newcommand{\mA}{\mG_\auxT}
  \newcommand{\bA}{\bG_\auxT}

  \newcommand{\tA}{\tG_\auxT}
  \newcommand{\qA}{\qG_\auxT}
  \newcommand{\rA}{\rG_\auxT}
  \newcommand{\sA}{\sG_\auxT}


  %%% boosted tetrad
  \newcommand{\kS}{\kG_\spcT}
  \newcommand{\lS}{\lG_\spcT}
  \newcommand{\mS}{\mG_\spcT}
  \newcommand{\bS}{\bG_\spcT}

  \newcommand{\tS}{\tG_\spcT}
  \newcommand{\qS}{\qG_\spcT}
  \newcommand{\rS}{\rG_\spcT}
  \newcommand{\sS}{\sG_\spcT}

                                                                               %:: \vspace{30pt}

  
  %%% l-spinor frame
  \newcommand{\SLi}{\bar{\tens{\iota}}}     
  \newcommand{\SLo}{\bar{\tens{\omicron}}}  
  
%  %%% coordinate indices
%  \newcommand{\bmu}{{\bar\mu}}
%  \newcommand{\bm}{{\bar m}}


                                                                               %:: \end{minipage}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


  \DeclareOption{PlainTensors}{
     \renewcommand{\tens}[1]{{\mathrm{#1}}} % tensor wrapper     %:skip:
     \renewcommand{\mtrc}{g}                % metric             %:skip:
     \renewcommand{\grad}{\mathrm{d}}       % gradient           %:skip:
     }

\ProcessOptions
