How much physics a mathematician needs to know to study GR?

Question

I'm intending to study General Relativity on my own. The thing is, my physics background is not very strong. I know classical mechanics and I know some electromagnetism. I'm familiar with Gauss' law, Ampere's law, RLC circuits, ... but I still have problems with the intuition behind concepts like 'momentum'. I know that momentum is nothing but $p=mv$ and I know that the change in momentum is associated to a force acting on the particle by the equation $F=\displaystyle {\mbox d p \over \mbox d t}$ but I'm not sure if my background is enough.

I know some differential geometry and this semester I'm going to take a course in topological manifolds. I guess my mathematical background is strong enough for GR. But I don't know where I should start. I know the basics of special relativity, but I only know the basics, I don't know every details that a physics student must know. So, where do you think I should start from?

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user some1.new4u

Comments

Possible duplicates: physics.stackexchange.com/q/14074/2451 and physics.stackexchange.com/q/14457/2451 Related: physics.stackexchange.com/q/15002/2451

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user Qmechanic

Answer 1

As you're a mathematician, I'll just discuss the Physics prerequisites .

1. Newtonian Mechanics. You seem to know this .
2. Lagrangian Mechanics . Unarguably the most elegant formulation of all of Classical Mechanics .
3. Hamiltonian Mechanics . An uglier, but equally useful (almost), formulation .
4. Newtonian Gravity . The theory of gravity as an inverse square field with the "charge" as the mass .
5. Maxwellian Electromagnetism . A Lorentz invariant formulation of EM. Formulated way before Lorentz Invariance and Lorentz Symmetry were ever thought of.
6. Special Relativity (the Minkowskian formulation, of course, is needed here .) . Of course .

As you're a mathematician, you'd probably like Wald, R.M's General Relativity, a mathematically rigorous textbook . Though I don't like it as it is too rigorous . I prefer Ludvigsen's General Relativity: A geometric approach. But that isn't a book a mathematician would like .

Comments

Sounds like I will have to spend a long time studying all those, right? I know Newtonian gravity to some extents. I have also completed a course on Astronomy 101 on coursera.org from Duke university. Do you think that's enough background for 4.? Would you please suggest some easy books for these subjects?

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user some1.new4u

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@some1.new4u: For Newtonian Mechanics & Maxwellian Electromagnetism & Special Relativity (in Einstein's approach), you can read Jewett and Serway Physics for Scientists and Engineers (With Modern Physics). It doesn't cover Lagrangian Mech, Hamiltonian Mech, or GR, though .

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user Dimensio1n0

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@some1.new4u: For Special Relativity in Minkowski 's approach, Ludvigsen covers it, I think Wald does too, can't remember . Lagrangian Mech and Hamiltonian Mech: Wikipedia is enough .

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user Dimensio1n0

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I would not call Wald's book rigorous mathematically. Surely very technical, but not rigorous. In my opinion you learn much better from books like Wald's than from mathematically rigorous books.

Answer 2

If you know freshman calculus (derivatives and integrals) and freshman physics you should be able to handle a general relativity course or self-study.

The important part is graphing the space-time effects and being able to muster the thought experiments for time dilation. The thought experiments are largely conceptual and provide the intuitive understanding of the mechanics of GR.

Similarly, length contraction formulas and concepts can be understood with a reasonable amount of comfort with a basic understanding time dilation. Since both are related, you'd be a hop, skip, and jump away from the basics and foundations of GR within a few months of self-study. Further, there are plenty of free online resources covering this topic (Stanford being one of them).

Look for MIT or Stanford videos on General Relativity on YouTube.

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user Mahesh Kommareddi

Comments

This seems more to be for SR than GR . Such basic knowledge is hardly enough for GR. Note: The OP is a mathematician, not a layman . He definitely knows "freshman calculus". : )

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user Dimensio1n0

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@Dimension10 Correction noted, thanks. I didn't mean to offend the author in recommending "freshman calculus". I was just writing to the general audience that might read this and be interested in the topic.

This post imported from StackExchange Physics at 2014-03-24 03:32 (UCT), posted by SE-user Mahesh Kommareddi