Mathematical prerequisites for general relativity

In summary: If you are starting from scratch, you can check out some online notes from Sean Carroll. He has a great book called "Einstein's gravitational theory" that covers most of the maths necessary.
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accdd
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What mathematical topics do I need to know to start studying general relativity?
From which textbooks can I learn them?
I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and some special relativity.
 
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Your pre-requisites are fine and intro gr texts will teach you about the mathematical machinery you need. Don't bother learning diff geom from a maths book at this stage (unless you want to, of course). If you can learn to push around tensor indices without thinking, you're halfway there.
 
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  • #3
accdd said:
What mathematical topics do I need to know to start studying general relativity?
From which textbooks can I learn them?
I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and some special relativity.
I agree with @ergospherical, with your maths knowldege you should get started on GR directly. Sean Carroll's book is a good introduction that you should be able to work from. There are also these MIT lectures from a graduate course in GR that are very good. They start with a review of SR from the geometric viewpoint:

https://ocw.mit.edu/courses/8-962-g...ction-and-the-geometric-viewpoint-on-physics/
 
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ergospherical said:
If you can learn to push around tensor indices without thinking, you're halfway there.
The other half is learning to swallow vectors as differential operators. :oldgrumpy:
 
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Ibix said:
The other half is learning to swallow vectors as differential operators. :oldgrumpy:
Only the tangent vectors. The cotangent vectors are linear maps from local first order linear differential operators to the real numbers. 😁

Other than that, I can just repeat what has been said: You need multivariable calculus, linear algebra, some differential equation solving skills. Apart from that most introductory books will include what maths you need. Of course, nothing stops you from reading about differential geometry in some well chosen mathematical methods text. It is also quite applicable to other areas in physics.
 
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If you are talking Wald's level (the most hardcore one). You will need Riemannian geometry. People would also read Wald GR together with John M lee's intro smooth manifolds.

I don't think you need to concern too much if you were not using such a hardcore book. People just learn the maths when they read from their physics textbook
 

FAQ: Mathematical prerequisites for general relativity

1. What is the significance of mathematical prerequisites for general relativity?

The mathematical prerequisites for general relativity are essential for understanding the theory and making accurate predictions. Without a solid understanding of the mathematical concepts involved, it is difficult to fully comprehend the complexities of general relativity.

2. What are the main mathematical concepts needed for general relativity?

The main mathematical concepts needed for general relativity include tensor calculus, differential geometry, and the theory of manifolds. These concepts are used to describe the curvature of spacetime and the motion of objects within it.

3. Do I need advanced mathematics knowledge to understand general relativity?

Yes, a strong foundation in advanced mathematics is necessary to fully understand general relativity. This includes knowledge of calculus, linear algebra, and differential equations.

4. Can I learn the mathematical prerequisites for general relativity on my own?

While it is possible to learn the mathematical prerequisites for general relativity on your own, it is recommended to have a background in advanced mathematics and to seek guidance from a qualified instructor or textbook.

5. How important is it to have a strong grasp of mathematics for studying general relativity?

A strong grasp of mathematics is crucial for studying general relativity. It is the language in which the theory is expressed and without it, it is difficult to fully understand and make accurate predictions in the field of general relativity.

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