Introduction Math for General Relativity - Engineers

[valenumr]

Any recommendations on introductory math related to general relativity for someone with an engineering background? I've been trying to learn the necessary math, but I'm having a hard time figuring out what I should be studying. Basic background for me is college physics
I and ll, all the calculus plus differential equations, linear algebra all day, and some masters work in applied mathematics. I see one book by skinner, but it seems conceptual, and I'm more of a math person. I'm interested in learning the basic math necessary to wrap my head around the the theory. I've been going on my own for a while, but I'm not really getting where I need to be.

 

[PeroK]

Any recommendations on introductory math related to general relativity for someone with an engineering background? I've been trying to learn the necessary math, but I'm having a hard time figuring out what I should be studying. Basic background for me is college physics
I and ll, all the calculus plus differential equations, linear algebra all day, and some masters work in applied mathematics. I see one book by skinner, but it seems conceptual, and I'm more of a math person. I'm interested in learning the basic math necessary to wrap my head around the the theory. I've been going on my own for a while, but I'm not really getting where I need to be.

You could take a look at Hartle, which is probably the least mathematically demanding introduction to GR:

https://www.cambridge.org/highereducation/books/gravity/F9085ABB699F7A3A05ADD0B3930D98E0#overview

Alternatively, this series of (graduate) lectures from MIT:

 

[valenumr]

You could take a look at Hartle, which is probably the least mathematically demanding introduction to GR:

https://www.cambridge.org/highereducation/books/gravity/F9085ABB699F7A3A05ADD0B3930D98E0#overview

Alternatively, this series of (graduate) lectures from MIT:

Thanks, I'll check it out. I'm really looking for foundational math.

 

[PeroK]

Thanks, I'll check it out. I'm really looking for foundational math.

The core of GR is differential geometry and differentiable manifolds. There are some GR-specific notes here:

https://uchicago.app.box.com/s/vabknygqmfkzngv44ru2st30ehpa5ozi

However, I don't believe you need to study that before you embark on Hartle or the MIT lectures. Only really if you want to take the subject further.

The other point is that you are never going to digest GR unless you fully understand SR. From a practical point of view that's an essential prerequisite. How's your SR?

 

[valenumr]

The core of GR is differential geometry and differentiable manifolds. There are some GR-specific notes here:

https://uchicago.app.box.com/s/vabknygqmfkzngv44ru2st30ehpa5ozi

However, I don't believe you need to study that before you embark on Hartle or the MIT lectures. Only really if you want to take the subject further.

The other point is that you are never going to digest GR unless you fully understand SR. From a practical point of view that's an essential prerequisite. How's your SR?

My SR is "okay", but still studying. I find it more digestible as I have the math tools to take care of it. Still working on QED though.

 

[robphy]

The core of GR is differential geometry and differentiable manifolds. There are some GR-specific notes here:

https://uchicago.app.box.com/s/vabknygqmfkzngv44ru2st30ehpa5ozi

However, I don't believe you need to study that before you embark on Hartle or the MIT lectures. Only really if you want to take the subject further.

The other point is that you are never going to digest GR unless you fully understand SR. From a practical point of view that's an essential prerequisite. How's your SR?

Since these are Geroch's Differential Geometry notes,
here are his General Relativity notes [among other items]
http://home.uchicago.edu/~geroch/Course Notes
and Problem Sets with solutions
http://home.uchicago.edu/~geroch/Problem Sets
and other topics at
http://home.uchicago.edu/~geroch/Short Topics

 

[haushofer]

This book is also nice and approachable:

https://www.amazon.com/dp/0199573646/?tag=pfamazon01-20

 

[bhobba]

Well, if you want a book written by an actual engineer that is short and to the point, then Dirac's book is my suggestion:
https://www.amazon.com.au/dp/069101146X/

It is sometimes forgotten Dirac was an Electrical Engineer before doing math at Bristol then doing post-graduate work at Cambridge.

A bit of esoteric history, but the book is still good as an introduction. Not the way I would do it, but Dirac had his style.

Thanks
Bill

 

[romsofia]

I used this book by Burke to help my dad (former EE) understand some relativistic/cosmological ideas he has seen on the science channel shows (looks like they updated it! I have a copy made back in the 80s):
https://www.amazon.com/dp/0486845583/?tag=pfamazon01-20

Looks like it is on sale too.

 

[Demystifier]

Well, if you want a book written by an actual engineer that is short and to the point, then Dirac's book is my suggestion:

If someone asked about string theory for historians, would you then recommend Witten?

 

[valenumr]

If someone asked about string theory for historians, would you then recommend Witten?

I won't remotely claim to understand string theory, but I read enough to know that is funny, I don't care who you are.

 

[valenumr]

Well, if you want a book written by an actual engineer that is short and to the point, then Dirac's book is my suggestion:
https://www.amazon.com.au/dp/069101146X/

It is sometimes forgotten Dirac was an Electrical Engineer before doing math at Bristol then doing post-graduate work at Cambridge.

A bit of esoteric history, but the book is still good as an introduction. Not the way I would do it, but Dirac had his style.

Thanks
Bill

Interesting, I have degrees in electrical and computer engineering, and about 2/3 of a master's in applied math. But my career ended up more on the computer side to be honest. I'm trying to get previews of the many suggestions here. Thanks all.

 

[paralleltransport]

Actually the math you have is fine and enough to start studying GR from one of the introductory textbook or lecture courses online.
(for example this book online is free and pretty well written http://fma.if.usp.br/~mlima/teaching/PGF5292_2021/Carroll_SG.pdf).

You said you had introductory physics. What you likely lack is being comfortable with index manipulation, 4 vectors & einstein summation notation, which most GR textbook will pretend they can teach you (they really don't, it's sink or swim), as well as E&M/classical field in relativistic covariant notation.

For that I really liked Griffiths last chapter from Electrodynamics book. I'm sure you can find the solution manual somewhere has lots of good problems to practice.

 

[valenumr]

Actually the math you have is fine and enough to start studying GR from one of the introductory textbook or lecture courses online.
(for example this book online is free and pretty well written http://fma.if.usp.br/~mlima/teaching/PGF5292_2021/Carroll_SG.pdf).

You said you had introductory physics. What you likely lack is being comfortable with index manipulation, 4 vectors & einstein summation notation, which most GR textbook will pretend they can teach you (they really don't, it's sink or swim), as well as E&M/classical field in relativistic covariant notation.

For that I really liked Griffiths last chapter from Electrodynamics book. I'm sure you can find the solution manual somewhere has lots of good problems to practice.

Thanks. The indexing is really foreign for sure, but I'm slowly getting used to it. It's definitely not at he point for me where it feels natural.

 

[Demystifier]

Thanks. The indexing is really foreign for sure, but I'm slowly getting used to it. It's definitely not at he point for me where it feels natural.

Wait to see the index-free notation, it takes even more effort to get used to it.

 

[valenumr]

Wait to see the index-free notation, it takes even more effort to get used to it.

Great (sarcasm)

 

[paralleltransport]

Another option on learning index notation is to read landau lifshitz vol. 2, also freely online. The first 30 pages or so covers relativity and index notation at a level that is a good starting point for any GR textbook. The presentation is very clear, it's actually my favorite treatment of relativity and E&M so far. It has a bit of a "mature" style, so it takes time to get used to, but I think it really reflects the principle of symmetry as a guiding principle.

http://fulviofrisone.com/attachments/article/209/Landau L.D. Lifschitz E.M.- Vol. 2 - The Classical Theory of Fields.pdf