debugmode: true;

linel: 150;

load("ctensor");

dim: 4;
cframe_flag: false;
ct_coords: [u, r, theta, phi];

depends([U, V, _beta, _gamma], [u, r, theta]);

lg : zeromatrix(4, 4);
lg[1, 1] : V * r^-1 * exp(2 * _beta) - U^2 * r^2 * exp(2 * _gamma);

lg[1, 2] : exp(2 * _beta);
lg[2, 1] : exp(2 * _beta);

lg[1, 3] : U * r^2 * exp(2 * _gamma);
lg[3, 1] : U * r^2 * exp(2 * _gamma);

lg[3, 3] : - r^2 * exp(2 * _gamma);
lg[4, 4] : - r^2 * exp(- 2 * _gamma) * sin(theta)^2;

/* Load metric and compute inverse */
cmetric();

/* For some reason some components must be simplified by hand ... */
ug[2,2] : expand(ug[2,2]),simp;

/*
    Calculate Christoffel symbols
    mcs[i, j, k]: Christoffel symbols of the second kind (one upper index - k)
*/

christof(false);
ricci(false);