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Prerequisites for General Relativity (Advice needed)

Summary: At this point, I am thorough with single variable, multivariable calculus, differential equations, linear algebra and basic concepts of point-set topology and tensor analysis. To learn General Relativity along-with its mathematical rigor, what are the topics I should first be thorough and in what order should I learn them?

I am currently studying as a second year undergraduate. I am, along-with my professors, planning to organize a lecture series to be lectured by me on General Relativity. I would personally like the lecture to include the mathematics of the topic rather than it being superficial. The lecture series is going to be organized in January next year so I have about three months at hand. But at this point I am thorough with only those topics I have mentioned in the summary. What more topics should I learn before starting to learn GR? Also in what order should I learn them so as to understand each topic thoroughly?
 

Orodruin

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You are planning to give lectures in GR three months after not knowing anything about it as a second year student? If so, forget it. GR is a subject typically considered difficult by fourth year university students.
 

DEvens

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As Orodruin says, this seems overly ambitious. It might be reasonable for you to give a single lecture, half hour or an hour, reporting on what you have learned in three months.

But before you can be "thorough" with GR you will need a lot of differential geometry. I took a full year class on differential geometry, then a full year class on relativity. And I realized at that point that I had barely gotten my toes wet. I then did an honors project with my prof from the relativity class, and was able to stumble through a 20 minute lecture. It was not the nicest experience of my life. :frown:

You could start with Weinberg's _Gravitation and Cosmology_. There are some accessible topics in there for your level of math. When you get to the parts about metrics and connections and Einstein tensors and such, you should discuss with your prof about some other texts that will give you much more background.
 
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What more topics should I learn before starting to learn GR? Also in what order should I learn them so as to understand each topic thoroughly?
Well you already seem to have everything you need to start learning, basically anyone with the rudiments of algebra and geometry can start learning GR, but imo it's very unlikely that you'll be able to present anything other than a cursory overview of the subject.

If you want maths I'd say read Schutz
https://www.cambridge.org/gb/academic/subjects/physics/cosmology-relativity-and-gravitation/first-course-general-relativity-2nd-edition

if you want physics, take Efstathiou et al.
http://www.cambridge.org/es/academic/subjects/physics/cosmology-relativity-and-gravitation/general-relativity-introduction-physicists?format=HB&isbn=9780521829519

Personally I like both, but learning an entire field is not something you can do quickly.
 

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