- #1
shinobi20
- 277
- 20
I have been reading the book Spacetime and Geometry by Sean Carroll, especially Ch. 2 Manifolds and Ch. 3 Curvature. I'm just wondering are there any lecture notes or books with lots of practice problems (with solutions or at least answers the better) that is suitable for physicist?
To give an example, in section 2.3, the book talks about how the tangent space is defined and how tangent vectors are constructed; exercises might be of the form, given a coordinate transformation find this and that, or show that this and that are orthogonal, etc. I'm seeking for exercises that allows for practice using these concepts that are relevant to physicist. Some people might recommend just plain pure math references where you need to prove this and that, but that is not what I'm looking for.
The exercises should focus more on the "math used in GR" (but still tailored for physicist) as opposed to the physics of GR like, find the gravitational time dilation of..., compute the variation of the lagrangian and find the EOM, etc.
So in short, exercises that are relevant to Ch. 2 Manifolds and Ch. 3 Curvature of the book. I already know many GR resources like Zee, Nightingale, Schutz, Ohanian, Rindler, Blau, Tong, etc. but their exercises are either too few or have no immediate relevance to the topics mentioned above. I find that exercises related to the math of GR to be not abundant, at least in the context of GR books that I know of.
To give an example, in section 2.3, the book talks about how the tangent space is defined and how tangent vectors are constructed; exercises might be of the form, given a coordinate transformation find this and that, or show that this and that are orthogonal, etc. I'm seeking for exercises that allows for practice using these concepts that are relevant to physicist. Some people might recommend just plain pure math references where you need to prove this and that, but that is not what I'm looking for.
The exercises should focus more on the "math used in GR" (but still tailored for physicist) as opposed to the physics of GR like, find the gravitational time dilation of..., compute the variation of the lagrangian and find the EOM, etc.
So in short, exercises that are relevant to Ch. 2 Manifolds and Ch. 3 Curvature of the book. I already know many GR resources like Zee, Nightingale, Schutz, Ohanian, Rindler, Blau, Tong, etc. but their exercises are either too few or have no immediate relevance to the topics mentioned above. I find that exercises related to the math of GR to be not abundant, at least in the context of GR books that I know of.
