GR: Practical Problem Sets w/ Solutions

[zwoodrow]

TL;DR Summary

Looking for an online collection of more down to earth calculation based questions for introductory gr

I have been learning gr on YouTube for the last few months. Most of the videos and the book I have focus on high level understanding. I can do all of the tensor calculus proofs. However simple questions like how you set up a velocity vector or measure proper time in schwarzschild are beyond me. Are there any books or online problem sets that walk you through how to do practical problems in gr?

 

[pervect]

I'm not quite sure what you're asking. Proper time is measured by idealized clocks - atomic clocks are pretty close to being ideal. Velocities in GR can be thought of as the rate of change of a coordinate with respect to proper time, or more abstractly as derivative operators.

Misner's "Precis of General Relativity", https://arxiv.org/abs/gr-qc/9508043, might possibly be of help, but since I don't actually know your question, it's hard to say.

Perhaps you'd find Possson's "A Relativists Toolkit" helpful, perhaps not. It does address the issue of physical interpretations of the theory, by means of the theory of congruences. While I found that approach very illuminating, I can't speak as to how popular it is, my sense is that others do not find it as helpful as I do.

I'd start with Misner's paper though. It might be totally unhelpful, but if you could explain why it was unhelpful we might get a better idea of what you're looking for.

 

[Orodruin]

This is a problem collection with solutions in both SR and GR. The level of the problems range from relatively basic to quite difficult. (The look inside feature will actually show you most of the SR problems - but none of the solutions.)

Full disclosure: The cover art may seem familiar from my avatar. That would be because I am one of the authors.