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I know all of special relativity but I also know it is not enough to study GR. The mathematics is very complex. I have “Spacetime and Geometry” by S. Caroll. He has described it GR well enough but I do not know some of the maths signs and symbols he uses. So what are the prerequisites I need to have in maths. Is there a book that covers those math topics? Or is ther a book on GR that is simple enough for me to understand? Please help.

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marked as duplicate by ACuriousMind Mar 15 '18 at 17:45

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  • $\begingroup$ I learned from Max Born's book during middle school. Obviously, it doesn't go into great depth, but it explains the basics at a very accessible level, and introduces the metric in an understandable way. During high school, I moved on to Schutz's book, which is closer to rigorous, but still doesn't require much mathematical sophistication. I recommend both highly. $\endgroup$ – Mike Mar 15 '18 at 18:12
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High school student here. I've tried reading Carroll as well, and I also found the math to be quite difficult. However, the good news is that not all of the math he introduces is necessary to understand the subject. It is possible to develop an intuitive understanding of GR without formal topology and differential geometry. For this, I recommend Hartle: https://www.amazon.com/Gravity-Introduction-Einsteins-General-Relativity/dp/0805386629. It's much more self-contained and accessible than Carroll. I learned about this book after I spent a year struggling through Carroll to learn GR, but I would have fared much better if I had started with this.

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For a general overview try Robert Geroch: "General relativity from A to B", it uses very little mathematics.

To get into the details you'll need to get familiar with partial differentiation and higher-dimensional calculus. The best book I know is D'Inverno: "Introducing Einstein's Relativity", there is no easier introduction to the mathematical aspects than this.

A book on classical mechanics may be better to start with in preparation for GR.

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Sean Caroll's book is one of the best books available for an introduction in GR. However, in order to trully understand what GR is about you will need to learn some essential things regarding differential geometry. As you may already know, S.Caroll's book "Spacetime and Geometry" covers these mathematical prerequisites in its first chapters, before introducing GR to the reader.

The first thing a physicist should do is try to find and learn only the trully essential elements of differential geometry needed to understand GR. In my opinion, it would be a waste of time to try and master differential geometry as a whole. For that purpose, I believe that the book you mention is very good as it has gathered these essential elements of diff. geometry and nothing additional (by additional I mean that nothing you learn from this book has no use in the study of GR).

Unfortunately, I do not have a better book in mind. The other books and material I know are all more advanced in the mathematics and, thus, harder for a high school pupil to cope with. I hope this helped a little.

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