General Relativity Textbook for an Engineer

[thepassenger48]

Hi,
I'm an engineering student looking to learn General Relativity... I was wondering which textbook would be the best for me?

I'm pretty well versed in classical physics, and in mathematics (linear algebra, multivariable calculus, partial differential equations), but I have no background in 4 vectors or differential geometry.

I guess some famous options are:
Gravity: An Introduction to Einstein's General Relativity by James B. Hartle
A First Course in General Relativity by Bernard Schutz
Exploring Black Holes: Introduction to General Relativity by Edwin F. Taylor
General Relativity by Robert M. Wald

 

[diazona]

I'm personally a fan of Hartle's book, but by the time I got to that I'd already studied special relativity a couple of times, which means I was pretty familiar with 4-vectors. I'd definitely suggest tackling SR before you start on GR.

 

[Daverz]

I agree, learn SR and then tackle Hartle. I would recommend the the red paperback first edition of Spacetime Physics. This has full solutions to the problem sets in the back, and is a better book IMO than the 2nd edition.

https://www.amazon.com/dp/071670336X/?tag=pfamazon01-20

Some Amazon sellers are clueless, so make sure the seller has the red paperback and not some other edition.

 

[Andy Resnick]

I disagree with insisting an engineer learn SR before GR.

thepassenger48, you did not say what kind of engineering student you are (i.e. mechanical, electrical, chemical, etc), but GR is a continuum field theory. If you have any experience in continuum mechanics- stress/strain relations, for example, you are well-placed to learn GR directly.

Differential geometry is critical for GR, but again, if you are comfortable with continuum mechanics, you are halfway there. I hear Wald's book is excellent, and I recommend Misner, Thorne and Wheeler (even though it's quite formidable) as having a very intuitive approach.

 

[malawi_glenn]

General Relativity: An Introduction for Physicists by M. P. Hobson

Is really nice, it will introduce you to the relevant SR and math before exploring general relativity.

 

[thepassenger48]

I disagree with insisting an engineer learn SR before GR.

thepassenger48, you did not say what kind of engineering student you are (i.e. mechanical, electrical, chemical, etc), but GR is a continuum field theory. If you have any experience in continuum mechanics- stress/strain relations, for example, you are well-placed to learn GR directly.

Differential geometry is critical for GR, but again, if you are comfortable with continuum mechanics, you are halfway there. I hear Wald's book is excellent, and I recommend Misner, Thorne and Wheeler (even though it's quite formidable) as having a very intuitive approach.

I'm a mechanical engineering student, and so I do have experience with stress/strain relations.
I also forgot to mention that I learned basic SR in college (time dilation, length contraction, relative mass, energy...etc), not just using the more advanced mathematics behind it.

Thanks for all the replies so far!

 

[Daverz]

I disagree with insisting an engineer learn SR before GR.

One will have to pick up SR along the way somehow. GR is going to be pretty confusing without it. I don't think Hartle's coverage is adequate for someone without previous exposure to SR at the level of 4-vectors and the energy-momentum relation.

 

[Andy Resnick]

One will have to pick up SR along the way somehow. GR is going to be pretty confusing without it. I don't think Hartle's coverage is adequate for someone without previous exposure to SR at the level of 4-vectors and the energy-momentum relation.

Why does the mathematical formalism have to be introduced via SR? Any engineer that has studied von Mises stress or Eulerian descriptions of flow will be able to pick up coordinate transformations, will 'get' covariant derivatives, Christoffel symbols, and how to handle tensor fields.

Just because we have been taught a set of topics in a particular order does not mean they *must* be taught in that order.

 

[Daverz]

Why does the mathematical formalism have to be introduced via SR? Any engineer that has studied von Mises stress or Eulerian descriptions of flow will be able to pick up coordinate transformations, will 'get' covariant derivatives, Christoffel symbols, and how to handle tensor fields.

That's only part of what one needs to understand GR. One needs to understand things like Lorentz invariance, the energy-momentum relation, and the physical meaning of the various components of the stress-energy 4-tensor. I suppose you could treat GR as pseudo-Riemannian geometry with metric signature (-+++), but at some point I think you'd need to discuss how physics works in the tangent spaces.

Just because we have been taught a set of topics in a particular order does not mean they *must* be taught in that order.

But they are always taught in that order, and all the textbooks use that order. You need to understand SR to be able to read the GR section of the books. Some GR books do a good job introducing SR, but I think Hartle expects some prior coursework in SR, which is why I suggested a supplemental book.