# How much physics a mathematician needs to know to study GR? [duplicate]

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?

The physics prerequisites to general relativity are really simple -- classical mechanics (Newtonian and Lagrangian), and special relativity. You need to know Newton's inverse-square law for gravity to appreciate general relativity physically, of course, but everyone knows this.

But there is still a notational math prerequisite to do general relativity well, which is the index notation for tensors. Mathematicians continue to use some sucky notation in which covariant tensors are written as functions of vectors and you have special notations for all sorts of tensor operations. This is bizarre and useless, the physics notation is a lot prettier and more useful.

Schutz is the best resource to refer to here.

• 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? – user66733 Aug 7 '13 at 15:43
• @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 . – Abhimanyu Pallavi Sudhir Aug 7 '13 at 15:46
• @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 . – Abhimanyu Pallavi Sudhir Aug 7 '13 at 15:47

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 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". : ) – Abhimanyu Pallavi Sudhir Aug 7 '13 at 15:54
• @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. – Mahesh Kommareddi Aug 7 '13 at 17:07