What math do I need to know to understand General Relativity

[dustball]

As the general math background for physics, V.I. Arnold's Mathematical Methods of Classical Mechanics is the best.

 

[AgentCachat]

I'm a 16 year old whose summer goal is two understand general relativity, but I'm lost on what math to have to understand it, I understand topological spaces and a topological manifold. but then it becomes more complicated math, and I know I simply don't understand because of the mathematics.

Calculus, basic linear(matrix) algebra, some differential equation familiarity, tensor algebra and analysis. Tensors are a part of differential geometry and are absolutely essential for understanding GR. Shaum's Tensor Calculus may be helpful, not really knowing more details. It includes needed linear algebra, and some other topics like tensor fields on manifolds. Its an outline, but should enable you to reach your goal. Don't be too discouraged. Einstein needed help on some math before he could complete his theory.

 

[dustball]

For SR try The Feynman lectures, vol. 1.

 

[rrogers]

This might seem strange but the most understandable book that I read was "The Large Scale Structure of Space-Time" by Hawkins and Ellis. Of course this was after I had gone through several other books that left an aura of mystery about a lot of things. In my mind that book nailed down a lot! Now I can read "Gravity" (which sort self reflects because it's weight certainly proves Gravity) without a hitch; and the details are just that details.

 

[Kevin McHugh]

Also, can you explain us why people care about the Hausdorff property? Can you explain why we care about compactness? Why do we let manifolds be second countable?

Sorry, but I want to gauge your topology knowledge.

I too am trying understand GR, and have read most of MTW. I can't recall any mention of the Hausdorff property in that tome. How is it necessary to understand curvature?

And to the OP, you can download Schutz for free from this site. It is a very good intro to GR.

 

[micromass]

I too am trying understand GR, and have read most of MTW. I can't recall any mention of the Hausdorff property in that tome. How is it necessary to understand curvature?

A spacetime is by definition Hausdorff. So it is already needed for the very definition of what we're working with. If MTW doesn't need the Hausdorff property, then MTW is just not a rigorous book. That's ok, I'm not saying that physics books need to be mathematically rigorous. But the OP mentioned Wald, and Wald definitely is rigorous (and does cover the Hausdorff property).

 

[Kevin McHugh]

A spacetime is by definition Hausdorff. So it is already needed for the very definition of what we're working with. If MTW doesn't need the Hausdorff property, then MTW is just not a rigorous book. That's ok, I'm not saying that physics books need to be mathematically rigorous. But the OP mentioned Wald, and Wald definitely is rigorous (and does cover the Hausdorff property).

Thanks for that micromass. You do learn something new every day.