Name: A first course in general relativity
ISBN: 9780521887052

A first course in general relativity

Clarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered.

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antogniniMar 2020

My personal recommendations for an undergraduate course in physics (based in large part off of my own undergrad curriculum):

Foundations:

1. Newtonian Mechanics by A.P. French (https://archive.org/details/NewtonianMechanics/mode/2up). This will give you a good foundation for what is to come.

2. Spacetime Physics by Taylor & Wheeler --- first edition if you can find it! It is much, much better than the second! Special relativity is conceptually strange, but mathematically pretty easy, so you can jump right into it after learning Newtonian mechanics. Have a little fun!

3. Electricity & Magnetism by Purcell. This book is a little unusual in that it derives magnetism from the laws of special relativity. This is the more natural approach than just asserting the laws of magnetism since magnetism is fundamentally a relativistic phenomenon.

4. Waves by Crawford. (https://archive.org/details/Waves_371/mode/2up) A bit hard to find in print, but a really excellent textbook. Waves are a fascinating topic because they come up in every area of physics, so a course focused around them has a huge number of applications.

5. Introduction to Quantum Mechanics by Griffiths. The best introduction to the topic you will find!

6. Thermal Physics by Kittel & Kroemer. I haven't actually found an introductory book on statistical physics that I'm crazy about, but this one isn't too bad.

That should last you some time. But once you're through with those and are looking for more, then here are some advanced topics:

7. Analytical Mechanics by Hand & Finch. This will teach you advanced Newtonian mechanics --- in particular Lagrangian and Hamiltonian dynamics. There is a chapter on chaotic dynamics towards the end, too. Another option here is Classical Mechanics by Goldstein.

8. Introduction to Electrodynamics by Griffiths. More advanced E&M than Purcell. If you want to go further, then there's always Classical Electrodynamics by Jackson.

9. Principles of Quantum Mechanics by Shankar. This spends more time on the mathematical foundations of QM than Griffiths does and goes into the path integral formalism and touches on relativistic QM towards the end of the book.

10. A First Course in General Relativity by Schutz. There are arbitrarily advanced texts on GR, but I'd recommend starting off with something friendly like Schutz.

11. An Introduction to Elementary Particles by Griffiths. Not super advanced mathematically, but it's a good thing to read over to prepare you for more advanced QFT texts. The first chapter is especially good as a history of the development of particle physics.

12. Quantum Field Theory in a Nutshell by Zee.

13. Modern Classical Physics by Thorne & Blandford. This is a tour de force. It's an enormous book but it really touches on everything that is left out by the above books. It covers optics, fluid dynamics, statistical physics, plasma physics, and more. (I'm currently reading through it and have only gotten through 6 chapters, but it's really an incredible textbook.)

14. Statistical Mechanics: Entropy, Order Parameters, and Complexity by Sethna. This is a really fun book, but almost all the material is in the problems.

Finally, and most importantly --- remember that physics is not a spectator sport! You must do problems. A lot of them --- and hard ones, too!

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tobmltMay 2018

First up, I am no expert, but I have traveled this road for a while so I'll share a bit. I see Susskind's theoretical minimum is plugged here. Good. That is a fantastic place to start. Start at the beginning. Skip nothing.

Leverage what you know against what you don't. You remember how to find an extremum of a function from Cal 1? The first order necessary condition for an extreme point is that the derivative of the function be zero. Remember that when you get to (deterministic) optimization and a gradient needs to be zero. Next with a constrained optimization you will see the reformulation of an objective function and constraints into one functional by using new variables (Lagrange "multipliers") so that when the gradient of this new functional is zero, not only are you somewhere in the intersection of the constraints and the objective, but you also meet the first order conditions necessary for an extremum to be found. (Second order sufficiency conditions (SOSC) are needed to show that you aren't instead at an inflection point but we are moving fast and breaking things)

Hmm, I didn't say that very well, but there is much intuition to be found in optimization problems. This will serve you well in physics.

Calculus of variations: Nail down cold how to derive the Euler Lagrange Equations for a functional. Hint, Apply the FONC (first order necessary conditions for an extremum) to the functional (now the Action) in question. See Lanczos "Calculus of Variations" (Dover Books) to sort out your initial questions and learn the smooth little trick with integration by parts. Susskind's first book comes in here.

Learn cold the integral of the Gaussian distribution and how to play around with it to find more complicated integrals. Orthogonality. Dot products and Fourier transforms have a lot in common! Fourier's trick is crucial. Oh man... have you got some fun in store here. Do not proceed to Quantum mechanics without having these tools at your disposal. Otherwise QM is just linear algebra over complex numbers together with complex amplitudes from circuits/naval architecture/ spring mass dampers in the frequency domain. (I mention all of these to raise awareness that complex amplitudes are not unique to QM) Supplement Susskind's second book with Griffiths intro QM book. Also see Griffeths E&M book for a great explanation of Fourier's trick and separation of variables in the chapter on special techniques... At least in the 1999 Third edition. (beware, it falls apart under little abuse!) Oh, and pick up the power series methods for solving tricky differential equations - don't learn it from the physicists. Learn it from "advanced differential equations materials". It's not bad in isolation - soon you will be computing recusion relations and bessel functions.

Soon it will be time to start thinking about field theory. A side quest is available if you want to get into fluid dynamics. Incidentally this is a great way to learn about uses for Green's functions... And if you dive deep, your first look at singular integral equations in field theory. But we will proceed dead ahead... to the book reviews (you will need more than one book):

https://fliptomato.wordpress.com/2006/12/30/from-griffiths-t...

https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-l...

Somebody else plugged 't Hooft here http://www.goodtheorist.science/ But there it is again. Now is a good time to speak of renormalization: There is an intro book out there: https://www.amazon.com/Renormalization-Methods-William-David...

It's okay but I have yet to derive more utility from it than from various field theory books. Oh and studying complex singular integrals in isolation is good too. Generally have some experience with contour integration around singularities.

See Sydney Coleman on symmetry breaking. (Man in the magnet, flip the sign of a term in your potential to get a mexican hat, see that the ground state is now different etc.)

There are tons of free resources out there for learning QFT. Use many sources. Expect to get stuck with any one of them. Bounce between them to un-stick.

Next up, differential geometry, tensors, and GR.... Google is your friend. I like Schutz's "a first course in general relativity" and really like Zee's Einstein Gravity book but I am working into this now and so my recommendations are running out. Check out this video as an intro to GR: https://www.youtube.com/watch?v=foRPKAKZWx8

To be inspired/get prepared for things to come get John Baez's Gauge-Knots_Gravity book: https://www.amazon.com/GAUGE-FIELDS-KNOTS-GRAVITY-Everything... and maybe Penrose's Road to Reality - which is like cosmology if the universe consisted of all the math and physics needed to understand all this math and physics. Baez's book probably has more exercises and is more focused in general. Stuff like this will help you see where more advanced mathematics comes in. By now you will be seeing manifolds and fibre bundles. Think of parameterizing a surface instead of a curve and see how a tangent bundle describes a whole new vector space - one vector space for every point in the manifold. Yang Mills... internal symmetry... ok I'd love to talk about how these are new expressions of ideas we've seen before but at some point up there we've passed my pay grade, I have to beg off until I can learn some more!

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r-bryanFeb 2018

I can recommend:

Bernard F. Schultz, _A first course in general relativity_

It's accessible to undergrads! (who have studied SR, vector calculus, electrostatics).

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catnaroekJan 2018

I learnt a lot from “Introducing Einstein's Relativity” by Ray d'Inverno and “A First Course in General Relativity” by Bernard Schutz. However, they are by no means leisurely reads. You need to be prepared to expand your mind (both your physical intuition and mathematical technique) and work very hard (you don't learn just by reading theory, you need to solve exercises and perform long calculations).

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Hydraulix989Oct 2016

For GR, I really liked Bernard Schutz's "A First Course in General Relativity" -- I read it from cover to cover.

Extremely lucid explanations of some very complex topics, and reading it for the first time blew my mind.

This book "teaches" you well (compared to other books where I feel like I really am putting in a ton of mental effort just to learn what the book is trying to say, much like reading mathematics articles on Wikipedia), and it still manages to move fast.

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codethiefOct 2022

I realize this is one of the most difficult points to understand about relativity.

The question this paradox comes down to is, when are you comparing your watches? The two observers (the spaceship and you) won't be able to agree on what it means for two events to occur at the same time. Once you take this into account you will realize there is no contradiction and the POVs of the two observers are indeed symmetric as expected from the word "relativity".

For more on this check out e.g. Bernhard Schutz's "A First Course in General Relativity". IMO it's a rather terrible book as far as General Relativity goes but the first chapter, which is about Special Relativity (~25 pages), is fantastic and is was what helped me finally understand SR and, in particular, the paradoxes.

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