Do you have the option to study physics, if not astrophysics? If you are looking at the undergraduate level, I don't think there is too much advantage in specializing too much into astrophysics. After you have your physics degree, you can then --- if you still wish and there's a mean to do it...
I don't remember if this can be found in the book --- but O'Neill's text "https://www.amazon.com/dp/0486493423/?tag=pfamazon01-20" has a very detailed study of Kerr geodesics.
https://www.amazon.com/dp/0387260781/?tag=pfamazon01-20 (Foster and Nightingale) is pretty nice as an introduction to the subject, perhaps supplement it with a more standard text like Carroll's.
Michell-Laplace dark star. Note the crucial difference though: for dark star light can leave its surface much like a ball can leave Earth's surface -- but it will fall back down due to the strong gravity. In GR, light cannot ever leave the horizon.
The book "Physics for Mathematicians: Mechanics I" by Spivak spends a great deal of Chapter 1 just to discuss Newton's laws of motion. You may be interested.
LOL :biggrin: Circuit was THE reason why I decided not to study physics for my A-Level (I got pretty bad experience when learning it during high school science -- and I soldered my finger too. That was painful.), and as a result also not majoring in physics in university, and majored in math...
The beautiful [math] book "The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity" by Naber has an appendix that discusses topology for Minkowski spacetime.