(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[1]

(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.)

[2]

[3]

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 [1] 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.

[2] 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.

[3] 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.

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# General Relativity Problem Questions

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