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I'm a high school student investigating how one can predict the mass and spin of the product of a binary black hole system. I'm fluent in Calculus (Single Variable), Number Theory, and Graph Theory, and High School Physics.

I understand that Black Holes involve Angular Momentum, Scharzwild Radii, Einstein's Field Equations and much more. However, I have no knowledge on any of these topics. As such, it's quite overwhelming and I'm unsure where to begin (I don't have any, if at all, experience in Astronomy). Despite this hurdle, I'm prepared to learn any new ideas/concepts required to make significant progress on my research.

What books/articles/papers/topics should I read to begin understanding black holes and to begin making progress on my research?

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  • $\begingroup$ step 1: read any textbook on introductory general relativity. Carroll is allright. $\endgroup$ – AccidentalFourierTransform Nov 27 '19 at 1:32
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    $\begingroup$ Why did you pick this topic? The complexitIes of numerical relativity were Ph.D. research topics as recently as last decade. $\endgroup$ – G. Smith Nov 27 '19 at 1:54
  • $\begingroup$ Black Holes are such an exciting phenomenon; Plus, as a mathematics major in HS, I seek to apply my Mathematical Ingenuity to hopefully understand a famous physical phenomenon; $\endgroup$ – DarkRunner Nov 27 '19 at 1:57
  • $\begingroup$ I suggest starting with gravitational radiation from the Hulse-Taylor binary which is something a precocious high-school student can understand. $\endgroup$ – G. Smith Nov 27 '19 at 2:00
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    $\begingroup$ Number theory and graph theory are not particularly relevant to GR. Learn multi-variable calculus, differential equations, tensor calculus, differential geometry, etc. $\endgroup$ – G. Smith Nov 27 '19 at 2:32
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Don't let people tell you that you need to study 5 years of math to understand anything about general relativity. That's not true. I recently got a chance to teach a gen ed course at my college on special and general relativity, which was a lot of fun. Here is a reading list based on that course, which would probably be at a good level for you, or maybe slightly too easy. These books are all fairly cheap, except possibly the last 2. On special relativity:

  • Takeuchi, An illustrated guide to relativity, ch. 1-9 only
  • Stannard, Relativity: a very short introduction

After this we did mostly cosmology, not as much on black holes. A good book on GR at this level (although we didn't use it) is

  • Geroch, General relativity from A to B.

I wrote up my lecture notes on the course as a brief book, which is free online:

To get into a somewhat more mathematical treatment of black holes:

  • Taylor and Wheeler, Exploring black holes: introduction to general relativity

After that, a good GR book that is written for undergrads (not grad students, like most GR books) is:

  • Hartle, Gravity: an introduction to Einstein's general relativity

This would give you a pretty decent beginner's understanding of GR, including some of the math. At that point you would have more of a mental map of where to go next to achieve your goal. Good luck, and have fun!

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