Studying GR from a mathematical point of view

[JG89]

I want to study GR from a mathematical point of view but I know almost no physics. Is this possible? And what textbook would be more geared towards this?

Also, what are the math prerequisites that I need? I have studied up to analysis on manifolds, some linear algebra and multi-linear algebra, topology, and a tiny bit of ODE's. I don't think that this is enough, so what else should I pick up before I start studying GR?

 

[bcrowell]

GR can be studied at a variety of mathematical levels. There are presentations of GR using only simple algebra, and others using much more sophisticated math.

What does "almost no physics" mean? Does it mean that you don't know Newton's laws? That you haven't taken a freshman survey course?

I doubt that it's possible to understand GR mathematically if it's completely divorced from its physical context. It would be like learning arithmetic without knowing about money or counting apples.

 

[WannabeNewton]

https://www.amazon.com/dp/038790218X/?tag=pfamazon01-20

https://www.amazon.com/dp/0125267401/?tag=pfamazon01-20

https://www.amazon.com/dp/0199230722/?tag=pfamazon01-20

All three are textbooks on GR for mathematicians. That being said, I personally think it's a pointless venture. You should just learn physics. You would easily be able to understand the mathematical foundations of GR but you won't really acquire much if any of a deep understanding of GR if you don't know physics so I don't see the point. Regardless, in the end it's your call and the above three textbooks are well-regarded.

 

[JG89]

GR can be studied at a variety of mathematical levels. There are presentations of GR using only simple algebra, and others using much more sophisticated math.

What does "almost no physics" mean? Does it mean that you don't know Newton's laws? That you haven't taken a freshman survey course?

I doubt that it's possible to understand GR mathematically if it's completely divorced from its physical context. It would be like learning arithmetic without knowing about money or counting apples.

I have just taken a first year course in physics. But it wasn't a course that the physics majors were taking. It was an easier course, a level below. I guess I should just learn the physics then. I want to learn it, if possible, in such a way that it is a direct path to GR. I don't want to learn other things that aren't required to learn GR. Like if a first year math major wanted to learn about manifolds, a course in number theory doesn't matter. Something like that.

Also, should I learn more about ODE's and PDE's as well?

 

[maka89]

I have not had a course in GR, but if you want to learn it you should learn some classical mechanics first. I think you should be able to do this if you have had a university physics course, but it will be hard. ^^

This is a good book:
https://www.amazon.com/dp/0201657023/?tag=pfamazon01-20

Online lectures:
http://www.youtube.com/playlist?list=PLUHTGp7T4Zn_FU64InC0C8ZsejaxMtO3s

The lectures on special relativity contains some of Einsteins notation which is also used in GR.

EDIT: Don't know about those GR for mathematicians books mentioned by WannabeNewton though, they may be an easier route...

 

[Daverz]

You probably have more than enough math. For the Physics end, I think a sort of signifier of "enough knowledge" would be knowing what solutions to the wave equation look like. One would typically learn that in the second semester of an E&M course. Some Lagrangian mechanics is very helpful, though not absolutely necessary, but you need enough mechanics to understand the stress-energy tensor.

So I'd say, Mechanics on the level of Fowles or Symon and E&M on the level of Schwartz.

 

[bcrowell]

E&M and general relativity are the two classical field theories in physics. E&M is a lot easier. If you want to understand GR, it helps if you know your E&M first.