1. The problem statement, all variables and given/known data  (Low quality scan unfortunately: (1) contains Einstein notation for partial differentiation and (2) Einstein notation for the covariant derivative. e(r) and e(θ) are the components of v.)   Integral of (1-2m/r)^-1/2 dr, should be recognisable from Schrodinger’s solution 2. Relevant equations 3. The attempt at a solution My problem with the first  lies in the lack of knowledge of connection coefficients; I can happily deal with these in the 3 dimensional form but not in the unfamiliar 2D Kepler form. Part (1) was achieved, it is simple partial differentiation. Part (2) I couldn't, I was unable to work backwards due to no sign of partial differentiation in the final answers. Our lecturer only went over a single example of connection coefficients in a 3D case.  is more of "how I should proceed" question, with both x^1 and x^2 are both skewed by an angle theta. I can do the diagram and mark those covariant components, but otherwise am still scratching my head in regard to the ds^2 equations. It may actually be simple vector maths, and this I submit this question gingerly too.  Wondering how to do this integral, just need to know if there are approximations (or series) that I should use, turning the integral into something more palatable! I apologise in advance for any difficulty in answering these questions, which may in fact require some effort in providing the working. Of course, the help would be gratefully appreciated.