Are you an undergraduate student majoring in physics, engineering or math? Would you like some suggestions of books to learn about black holes and general relativity (GR) in more details, including the math involved? This blog post gives a couple of suggestions of textbooks to learn GR at different levels.
Gravity’s fatal attraction: Black holes in the universe. Mitchell Begelman & Martin Rees. For the undergrads that come to me interested in doing a undergraduate research project on black holes, I always recommend to read a couple of chapters from this book. Clear, non-technical description of black hole astrophysics, getting into a bit more detail than other expositions on the subject.
Black holes and time warps. Kip Thorne. A classic, must-read book for anybody wanting an in-depth account of the history of black holes and the main discoveries until the mid-nineties. Written by one of the leaders in the field and one of the pioneers of the LIGO observatories (he eventually got a Nobel prize for LIGO). Thorne gives a lot of historical details about the development of the theory of black holes and their observations.
Soft math, for physics, math or engineering students in the first or second year
Exploring black holes: Introduction to general relativity. Edwin Taylor & John Wheeler. Appropriate for first or second year undergraduates in physics, math or engineering. Very basic introduction to the general theory of relativity. Notions of calculus are recommended.
For physics students in the third or fourth years
This a standard introduction to general relativity for physics undergrads. It explores the effects of black hole spacetimes on particle orbits and light rays and has an emphasis on modern applications of the theory.
Suggested background: vector calculus, classical mechanics (at the level of Thornton & Marion).
Disclaimer: I use this textbook in my GR course.
A first course in general relativity. Bernard Schutz.
Another classic textbook which uses the more classic approach of first introducing and motivating Einstein’s equation, then solving it for a couple of basic spacetimes (Schwarzschild, Friedmann-Robertson-Walker).
Very basic discussion of the applications.
TBD: Carroll, MTW, Wald