/* Copyright (C) 2007 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.
 *
 * Computing Papapetrou's metric
 *
 */
("Papapetrou's metric is a nonsymmetric metric.")$
if get('ctensor,'version)=false then load(ctensor);
("We start with the covariant metric tensor.")$
ratfac:true;
dim:4;
ct_coords:[r,u,v,t];
lg:ident(4);
lg[1,1]:-A;
lg[2,2]:-r^2;
lg[3,3]:-r^2*sin(u)^2;
lg[4,4]:C;
lg[1,4]:W;
lg[4,1]:-W;
depends([A,C,W],[r]);
cmetric();
("Let us review the contravariant and covariant metric tensor:")$
ug;
lg;
("And let us calculate the connection coefficients.")$
("Note that Gamma(a,b,c)=Gamma(b,a,c) is no longer true!")$
derivabbrev:true;
("The next calculation can take quite a bit of time.")$
christof(mcs);
("We can also calculate the Ricci tensor for this metric.")$
ricci(true);
("Some components have a particularly simple relationship, e.g.,")$
ratsimp(ric[3,3]/ric[2,2]);
("For more information, see Moffat & Boal,")$
("Phys. Rev. D Vol. 11 No. 6, p1375.")$
/* End of demo -- comment line needed by MAXIMA to resume demo menu */