/* 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 Allnutt's type III perfect fluid metric
 *
 */

if get('ctensor,'version)=false then load(ctensor);
("Computing the Petrov classification of Allnutt's perfect fluid metric")$
("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);
g:4/9*exp(-3*x-4*y);
f:n^2*exp(-x)-g/3;
h:n^2*exp(-x+2*z)-n^2*exp(-x);
q:3/4*sqrt(6)*g^(-3/4)*exp(-x/4-z);
fri:matrix(
[-q/sqrt(2)*(f*exp(2*x)-exp(-2*x)),exp(2*x)/sqrt(2),          0,          0],
[-q/sqrt(2)*(f*exp(2*x)+exp(-2*x)),exp(2*x)/sqrt(2),          0,          0],
[                     -sqrt(2*g)*q,               0,3/sqrt(2*g),          0],
[                     -sqrt(2*h)*q,               0,          0,1/sqrt(2*h)])$
cmetric(false);
ug:invert(lg)$
nptetrad(false);
("We return to a coordinate base to compute the Weyl tensor")$
cframe_flag:false;
("The metric was computed for us by cmetric() already")$
weyl(false);
psi(true);
("And obtain the Petrov class")$
petrov();

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