Relativity Books for learning the maths used in learning Relativity

Are you looking for a text on the mathematics or for a text on relativity. Tensors and differential geometry is covered in many basic books (including mine), but they will generally not discuss the specifics of Lorentzian manifolds but instead keep to Riemannian geometry (where the metric is positive definite). The generalisation to pseudo metrics is rather straight forward though and any relativity text should discuss it.

 

I agree with Orodruin, get a good intro to GR that does a good job covering tensors. I recommend Schutz, A First Course in General Relativity.

If you want more mathematics and more depth, I suggest Frankel, Geometry of Physics, but it may be too much for a first pass.

 

For a GR intro, I really liked Foster and Nightingale's "A Short Course in General Relativity" because it progresses very naturally like this:
1. Curvilinear coordinate systems in flat space (e.g. polar or spherical)
2. Curvilinear coordinate systems for a curved surface in flat space (e.g. a spherical surface)
3. Specialize to remaining in that curved surface, and now you have a curved 2d space. Suddenly we are in GR land.
If you already know what the Jacobian is and how to transform between (x,y) and (r,theta) in flat 2d, then you can quickly get up to speed. If not, he introduces these things, and you'll just have to move a little more slowly.

 

Do you guys know what the basis of a tensor is?