What are Good Books on Tensors for Understanding Einstein's Field Equation?

[Alaindevos]

I'm looking for good books on Tensors.
I have "Introduction to Tensor Analysis and the Calculus of Moving Surfaces" from Pavel Grinfeld.
But i look for others.

[Mentor Note: Thread moved from the Relativity forum]

 

[Orodruin]

I’d say something, but I am biased.

 

[berkeman]

Then I'll say it...

https://www.amazon.com/Mathematical...attias-ebook/dp/B086H3LMZF/?tag=pfamazon01-20

 

[Orodruin]

Then I'll say it...
View attachment 342904
https://www.amazon.com/Mathematical...attias-ebook/dp/B086H3LMZF/?tag=pfamazon01-20

Say, that cover looks a lot like half of my profile image … weird!

 

[WWGD]

I'm looking for good books on Tensors.
I have "Introduction to Tensor Analysis and the Calculus of Moving Surfaces" from Pavel Grinfeld.
But i look for others.

Maybe you can tell us the perspective you're interested in: Math, Engineering, Physics /Relativity?

 

[Orodruin]

Maybe you can tell us the perspective you're interested in: Math, Engineering, Physics /Relativity?

If I was not hallucinating, this was originally posted in the relativity forum. That would indicate a physics perspective.

 

[WWGD]

If I was not hallucinating, this was originally posted in the relativity forum. That would indicate a physics perspective.

It only seems to be under "Science and Math textbooks".

 

[Orodruin]

It only seems to be under "Science and Math textbooks".

Yes, it was moved.

 

[WWGD]

Yes, it was moved.

And you liked to move it, move it.

 

[Orodruin]

And you liked to move it, move it.

Oh, I don’t have those kinds of powers any more …

But back to topic.

 

[berkeman]

If I was not hallucinating, this was originally posted in the relativity forum. That would indicate a physics perspective.

Good point; I did the move, and probably should have added a note to provide more context to the question. I'll add that into the OP now.

 

[berkeman]

And you liked to move it, move it.

I've tried several ways to parse this, but no joy so far. Not reverse-Polish, not Yoda-speak, not a single character typo that I can find... I'm getting dizzy.

 

[WWGD]

I've tried several ways to parse this, but no joy so far. Not reverse-Polish, not Yoda-speak, not a single character typo that I can find... I'm getting dizzy.

You and my therapist, who's jumped out of his window a few times, coincidentally in the middle of our sessions.

 

[berkeman]

You and my therapist, who's jumped out of his window a few times, coincidentally in the middle of our sessions.

But you know it's a first floor office, so you've never been impressed by this therapy tactic...

 

[WWGD]

Still, for anything related to Tensors from an Algebraic perspective, Keith Conrad from University of Connecticut has some great popularization
His Web Page:

https://kconrad.math.uconn.edu/

His expository papers:

https://kconrad.math.uconn.edu/blurbs/

 

[Alaindevos]

Some context. I just want to understand "Einsteins Field equation".
But as it is formulated in the form of tensors, i need to understand tensors.
Or abstract index notation ?
[ PS : I had vector calculus at University, but that's a different beast as the space was Euclidean]

 

[WWGD]

Some context. I just want to understand "Einsteins Field equation".
But as it is formulated in the form of tensors, i need to understand tensors.
Or abstract index notation ?
[ PS : I had vector calculus at University, but that's a different beast as the space was Euclidean]

John Lee's book on Riemannian Geometry may also be helpful .https://link.springer.com/book/10.1007/978-3-319-91755-9

 

[Ibix]

Some context. I just want to understand "Einsteins Field equation".
But as it is formulated in the form of tensors, i need to understand tensors.
Or abstract index notation ?
[ PS : I had vector calculus at University, but that's a different beast as the space was Euclidean]

In that case, almost any introductory GR book will provide enough of a grounding for you. I learned from Sean Carroll's online lecture notes originally, but you probably want to look at multiple sources. That one has the advantage of being free.

 

[Orodruin]

Some context. I just want to understand "Einsteins Field equation".
But as it is formulated in the form of tensors, i need to understand tensors.
Or abstract index notation ?

Abstract index notation is just a notational convention within tensor calculus/differential geometry. It is not a separate subject in itself.

[ PS : I had vector calculus at University, but that's a different beast as the space was Euclidean]

To quote Yoda:
"No! No different! Only different in your mind."

The way I like to introduce things like the covariant derivative, metric tensor, Christoffel symbols, etc., is to do it in Euclidean space using curvilinear coordinates. This makes the geometrical interpretation clearer and more grounded in what people are familiar with. It makes things a bit easier once you move on to general curved spaces to have that kind of intuition built. Then you can focus on the particulars like more general connections, curvature, etc.

 

[Alaindevos]

I currently own the book "Introduction to Riemannian Manifolds" (John Lee).
But it's above my head. I cannot read it. Understand all the symbols.
Nabla_underscore_X - nabla_underscore_Y - [X,Y]
The last i think is a commutator.
I need an introduction to this book ...

 

[Orodruin]

Understand all the symbols.

What do you mean by this? If you understand what all the symbols mean, getting the meaning should not be very difficult.

Note that you can also use the LaTeX features of the forum to post more readable equations, eg,

$$
T(X,Y) = \nabla_X Y - \nabla_Y X - [X,Y]
$$

 

[robphy]

You might find some helpful notes among:
Notes by https://en.wikipedia.org/wiki/Robert_Geroch
https://home.uchicago.edu/~geroch/Course Notes
https://home.uchicago.edu/~geroch/

 

[Muu9]