/* Copyright (C) 2004 Viktor T. Toth <http://www.vttoth.com/>
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2 of
 * the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be
 * useful, but WITHOUT ANY WARRANTY; without even the implied
 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
 * PURPOSE.  See the GNU General Public License for more details.
 *
 * Classification of Godel's universe
 *
 */

if get('ctensor,'version)=false then load(ctensor);
("Computing the Petrov classification of Godel's universe")$
("We use frames")$
cframe_flag:true;
("We set up the metric by hand")$
ct_coords:[t,x,y,z];
(lfg:ident(4),lfg[1,1]:-1,lfg)$
/*fri:matrix([1,0,e^(sqrt(2)*w*x),0],[0,1,0,0],
           [0,0,e^(sqrt(2)*w*x)/sqrt(2),0],[0,0,0,1]);*/
fri:matrix([a,0,a*exp(x),0],[0,a,0,0],[0,0,a*exp(x)/sqrt(2),0],[0,0,0,a]);
/*fri:matrix([a,0,a*exp(x),0],[0,a,0,0],[0,0,a,0],[0,0,0,a*exp(x)/sqrt(2)]);*/
cmetric(false);
ug:invert(lg);
weyl(false);
nptetrad(false);
psi(true);
("And obtain the Petrov class")$
petrov();

/* End of demo -- comment line needed by MAXIMA to resume demo menu */