/* ------------------------------------------
    Catalogue of Spacetimes
    
    Rotating coordinates for the Minkowski metric 
        
    Thomas Mueller, Frank Grave
    Visualization Research Center (VISUS)
    University of Stuttgart  
    
    Use with wxmaxima:
       batchload("rotMinkowski.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]:(1-omega^2*r^2/c^2)*c^2;
lg[1,3]:-r^2*omega;
lg[3,1]:-r^2*omega;
lg[2,2]:-1;
lg[3,3]:-r^2;
lg[4,4]:-1;

cmetric();

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

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

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

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

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