Bunch of codes for general relativity: e.g. calculation of: curvatures, trajectories, etc.
In files "Metrica di Schawrzchild.ipynb" and "Tensore_di_Rieman.nb" the Riemann tensor, the Ricci tensor and the scalar curvature of Ricci are calculated, starting from metric:
where the Christoffel symbols are given by:
In "geodetica sfera.nb" the geodesic on a sphere, which we know to be the circle of maximum radius, is calculated by solving the equation of motion:
In "E-F_coor.py" the radial trajectories of light are considered in coordinates that solve the apparent singularity in rs = 2M. From the Schawrzchild metric it is obtained:
where the + sign identifies the outgoing trajectories and the - the incoming ones
we can define:
"FRW_scale_factor.py" calculates the trend of the scale factor of the FRW metric, and the age of universe, in the case of a universe with different components. In the case of a closed universe, the analytical solution is present because the numerical solution presents problems due to the negative derivative
