% \filename{gemmac.tex} \version{21-nov-1997} needs work to clean up
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\overfullrule=0pt
%%%%% DISABLE FOR FINAL COPY:
%\newcommand{\Newpage}{\typeout{forced pagebreak after page:}\newpage}
\def\Int{{\scriptstyle\int}}
\def\Nu{\Vscr}
\def\Eq{Eq.}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% multiple contractions of p-vector against a q-form:
\def\leftcontractp#1{\mathop{\rlap{\hbox to 8pt{\hss$^{#1}$\hss}}%
\hbox{\vrule height0.5pt width8pt \vrule width0.5pt height6pt}}}
\def\rightcontractp#1{\mathop{%
\hbox{\vrule width0.5pt height6pt \vrule height0.5pt width8pt}%
\llap{\hbox to 8pt{\hss$^{#1}$\hss}}}}
\def\llangle{\langle\!\langle} \def\rrangle{\rangle\!\rangle}
\def\diff{\mathop{\rm diff}\nolimits}
%\newcommand{\Matrix}[2]{\begin{array}{#1}#2\end{array}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\gr{04.20.-q} % General Relativity
\def\cosmology{98.80.Dr} % Theoretical cosmology
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% relative observer arguments: two 4-velocities U, u
\def\Uu{(U,u)} \def\uu{(U,u)}
\def\uU{(u,U)}
\def\gammauu{\gamma}
\def\uu{(U,u)}
\def\gammau{\gamma\uu}
\def\nuu{\nu\uu}
\def\ptu{\tilde p\uu}
\def\ft{\tilde f}
%\def\Ft{\tilde F}
\def\Ftg{\tilde F\g}
\def\Ftu{\tilde F\uu}
\def\Au{A\uu}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% duality operations:
%\def\spp{spatially-projected}
\def\spp{spatial}
\def\dualp#1{{}^{\ast_{(\hbox{$\scriptstyle #1$})}} \kern-1pt}
\def\dual{\,{}^\ast{}\kern-1.5pt}
\def\leftdual{\,{}^\ast{}\kern-1.5pt}
\def\rightdual{{}^\ast{}\,}
\def\dual{\,{}^\ast}
\def\leftdual{\,{}^\ast}
\def\rightdual{^\ast{}\,}
\def\hook{\,\mathop{\breve{\,}}\nolimits\,}
\def\lefthook{\hook\kern-1.5pt}
\let\righthook=\hook
\def\hook{\,\mathop{\breve{\,}}\nolimits\,}
\def\lefthook{\hook\kern-1.5pt}
\let\righthook=\hook
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\Gb{\rlap{-}\hbox{$G$}} % fix later
%\let\G = \Gb
\def\Tb{\rlap{\hbox{--}}T} % fix later
\def\PLie(#1){\Lie(#1)}
\def\Pd{[\Pscr d]}
\def\Vec{} % \vec or not to \vec?
\let\covec=\overeq
%\def\emf#1{{\bf #1}} % for keywords
\def\emf#1{{\it #1\/}} % for keywords
\def\bfC{{\bf C}} \def\bfE{{\bf E}} \def\bfH{{\bf H}}
\def\bfL{{\bf L}}
\def\L{L}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% sub/super script stuff
\def\sub#1{_{\hbox{$#1$}}}
\let\subb=\sub
% SUBscript(Roman)Parenthesis / SUPerscript(Roman)Parenthesis:
\def\subr#1{_{\rm#1}} \def\supr#1{^{\rm#1}}
\def\subrp#1{_{\rm(#1)}} \def\suprp#1{^{\rm(#1)}}
\def\subp#1{_{(#1)}} \def\supp#1{^{(#1)}}
\def\lrs{\subrp{lrs}}
\def\refe{\subrp{ref}}
\def\refr{\subrp{refr}}
\def\ind{\subrp{ind}}
\def\fok{\subrp{des/fok}}
\def\thom{\subrp{thom}}
\def\geo{\subrp{geo}}
\def\gmag{\subrp{gm}}
\def\gyro{\subrp{gyro}}
\def\so{\subrp{so}}
\def\sc{\subrp{sc}}
\def\lies{\subrp{lie\sharp}}
\def\lief{\subrp{lie\flat}}
\def\lie{\subrp{lie}}
\def\tem{\subrp{tem}}
\def\fw{\subrp{fw}}
\def\fwcfw{\subrp{fw/cfw}}
\def\cfw {\subrp{cfw}}
\def\opt {\subrp{opt}}
\def\mol {\subrp{m\o l}}
\def\cov {\subrp{fw}}
\def\ncov {\subrp{lie}}
\def\sym {\subrp{sym}}
\def\perpp {\suprp{\bot}}
\def\parp {\suprp{||}}
\def\em {\suprp{EM}}
\def\g {\suprp{G}}
%\def\TR {\supr{TR}}
%\def\TF {\supr{TF}}
\def\TR {\suprp{TR}}
\def\TF {\suprp{TF}}
\def\H {\subrp{H}}
\def\E {\suprp{E}}
\def\M {\suprp{M}}
\def\adm {\subrp{ADM}}
\def\dR {\subrp{dR}}
\def\carter {\subrp{carter}}
\def\Thd{Thd}
% math subscript in parentheses:
\def\subpmath#1{_{(#1)}}
\def\MTW{Misner, Thorne and Wheeler}
\let\rcon=\rightcontract
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\long\def\begincomment#1\endcomment{}
\def\Cite#1{[#1]} % \cite is latex!!
\def\book#1{{\it #1\/}}
\def\art#1{\edef\test{#1} \edef\control{}%
\ifx\test\control {\bf{?!}}\else #1,\fi}
\def\pub(#1){(#1)}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\tabrule{\noalign{\hrule}}
\def\constant{\hbox{\it const}}
\def\gm{\hbox{\rm g}}
\def\gammam{\bfgamma}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FIGURES:
\def\bfig{\begin{figure}}
\def\efig{\end{figure}}
%\def\fig#1#2#3{\hrule \bfig \caption[#1]{#2} \label{#3}\efig \hrule }
\def\fig#1#2#3{\bfig \caption[#1]{{\narrower{#2}\par}}
\label{fig:#3}\efig
\typeout{Figure \thefigure.}}