Is EFE an equation to help us find the curvature cause by mass? Like the schwarzchild metric? In addition, is it a must to use polar coordinate for EFE to work since it contains dr? Can we used the ordinary Euclidean coordinate in minkoswki space for EFE? If we can't is it because there is no radius(dr) component in it? Cause curvature results in excess radius, right? Lastly, geodesic equation is the one that allows us to determine the path of an object in gravitational field by integrating it, right?