/* ------------------------------------------
    Catalogue of Spacetimes
    
    Schwarzschild metric 
        
    Thomas Mueller, Frank Grave
    Visualization Research Center (VISUS)
    University of Stuttgart  
    
    Use with wxmaxima:
       batchload("schwarzschild.wxm")
   ------------------------------------------ */

/* load ctensor package */
load(ctensor);

/* define coordinates to use */
ct_coords:[t,r,theta,phi];

/* start with the identity metric */
lg:ident(4);

lg[1,1]:c^2*(1-rs/r);
lg[2,2]:-1/(1-rs/r);
lg[3,3]:-r^2;
lg[4,4]:-r^2*sin(theta)^2;

cmetric();

/* calculate the christoffel symbols of the second kind */
christof(mcs);

/* calculate the riemann tensor */
lriemann(mcs);

/* calculate the ricci tensor */


/* calculate the ricci scalar */
ricci(mcs);

/* calculate the Kretschman scalar */
rinvariant();
ratsimp(%);