[Maxima-commits] CVS: maxima/share/tensor kruskal.dem, NONE, 1.1 tendemo.mac, 1.22, 1.23

[Viktor T. <vt...@us...>]

Update of /cvsroot/maxima/maxima/share/tensor
In directory sc8-pr-cvs16.sourceforge.net:/tmp/cvs-serv6711

Modified Files:
	tendemo.mac 
Added Files:
	kruskal.dem 
Log Message:

Added a new demo computing the Kruskal extension of Schwarzschild's metric.


--- NEW FILE: kruskal.dem ---
/* Copyright (C) 2008 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.
 *
 * The Kruskal extension of the Schwarzschild metric.
 *
 */
kill(allbut(props));

("Computing Kruskal's maximal extension of the Schwarzschild metric" )$

("We begin with redefinining the derivative of Lambert's W function.")$
gradef(lambert_w(x),lambert_w(x)/(1+lambert_w(x))/x);
("We want ctensor to perform rational factorization.")$
ratfac:true;
load(ctensor);
ct_coords:[T,R,u,v];
("This is Kruskal's metric in explicit form")$
r:2*(lambert_w((R-T)*(R+T)*exp(-1))+1)*G*M;
lg:ident(4);
lg[1,1]:-lg[2,2]:-16*G^2*M^2/(-T^2+R^2)*lambert_w(exp(-1)*(-T^2+R^2))/(lambert_w(exp(-1)*(-T^2+R^2))+1);
lg[3,3]:-r^2;
lg[4,4]:-r^2*sin(u)^2;
ric:zeromatrix(4,4);
cmetric();
christof(mcs);
ricci(false);
("Let us verify that this is a vacuum metric (Ricci tensor is zero)")$
radcan(ric);
("We now wish to express the metric coefficients as functions of r")$
kill(r);
("This is t: we can now plot the tt component of the metric")$
block([title: "The Kruskal-Szekeres metric coefficient for GM=1"],
/*plot3d([r*cos(u),r*sin(u),ev(subst((1-r/(2*G*M))*exp(r/(2*G*M))+R^2,T^2,ug[1,1]),G=1,M=1)],[r,0.01,5],[u,-%pi,%pi],['grid,50,15]));*/
/*plot3d([r*cos(u),r*sin(u),ev(subst((1-r/(2*G*M))*exp(r/(2*G*M))+R^2,T^2,ug[1,1]),G=1,M=1)],[r,0.01,5],[u,-%pi,%pi],['grid,7,7],[plot_format,gnuplot],[gnuplot_term,dumb],[gnuplot_dumb_term_command, "set term dumb 132 50"]));*/
plot2d(ev(subst((1-r/(2*G*M))*exp(r/(2*G*M))+R^2,T^2,ug[1,1]),G=1,M=1),[r,0,5],[plot_format,gnuplot],[gnuplot_term,dumb]));
/* End of demo -- comment line needed by MAXIMA to resume demo menu */

Index: tendemo.mac
===================================================================
RCS file: /cvsroot/maxima/maxima/share/tensor/tendemo.mac,v
retrieving revision 1.22
retrieving revision 1.23
diff -u -d -r1.22 -r1.23
--- tendemo.mac	21 Mar 2008 02:47:00 -0000	1.22
+++ tendemo.mac	1 Jul 2008 19:49:50 -0000	1.23
@@ -87,7 +87,7 @@
 print("4. The double divergence of R       14. Using a tetrad base"),
 print("5. Helicity in hydrodynamics        15. The Friedmann equations"),
 print("6. Magnetic field in plasma         16. Papapetrou's nonsymmetric metric"),
-print("7. Spinor algebra"),
+print("7. Spinor algebra                   17. The Kruskal extension"),
 print("8. The EM field tensor"),
 print("9. The Hodge star operator"),
 print("A. The Riemann and Weyl tensors"),
@@ -139,6 +139,7 @@
    else if sel=14 then demo(tetrad)
    else if sel=15 then demo(friedmann)
    else if sel=16 then demo(papapetrou)
+   else if sel=17 then demo(kruskal)
    else if sel#X and sel#x then print("*** Invalid entry, please try again")
    else sel:0
 )