Which text on differential geometry to supplement relativity

[Kostik]

I am looking to pick up one of these texts, but I don't really want to buy all three. Is there a considered favorite? Thanks in advance.

B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity

T. Frankel: The Geometry of Physics

B. Schutz: Geometrical Methods of Mathematical Physics

 

[vanhees71]

I found it sufficient to read the introduction to pseudo-Riemann geometry provided in the GR textbooks. In this respect my favorite is

https://www.amazon.com/dp/0521010691/?tag=pfamazon01-20

 

[robphy]

It depends.
Those three focus on different topics and will appeal to different audiences. What kind of relativity course of study are you pursuing?
What relativity text are you using?

 

[bapowell]

My favorite differential geometry reference is the series of books by John Lee: https://www.amazon.com/dp/0387983228/?tag=pfamazon01-20

Frankel is not a differential geometry text per se, but more of a grab bag of advanced geometry, topology, and algebra needed in several areas of mathematical physics. In this role, I recommend Nakahara over Frankel.

 

[Kostik]

It depends.
Those three focus on different topics and will appeal to different audiences. What kind of relativity course of study are you pursuing?
What relativity text are you using?

robphy: I am refreshing my E&M / SR with Ohanian's E&M text. I want to study GR and have several books - Schutz (old edition - small green paperback), D'Inverno, Weinberg, Ohanian-Ruffini, Dray and Zee. I was planning to read Weinberg first to get "to the physics" as quickly as possible.

I have a PhD in math but in analysis and number theory. My background in geometry and topology is weak, but I am generally good with proofs and mathematical "maturity". I was considering getting a supplementary text as noted above, since I find I often sidetrack myself to put the math on solid footing if the physics text doesn't do so. Thanks.

 

[Ben Niehoff]

I'm partial to Nakahara, especially if you're comfortable with a more "mathy" treatment.

 

[robphy]

For a supplement to relativity, I would prefer a book that made explicit connections with relativity.
"How can mathematics be used to model the physics?"

The three books you listed are written by mathematically-oriented relativists
It's difficult to pick one.
I offer my opinions as a physicist interested in geometrical formulations.

If the focus is relativity, I would choose
B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity
or
F. de Felice & C.J.S. Clarke: Relativity on Curved Manifolds

If the focus is relativity and other physical topics, I would choose
T. Frankel: The Geometry of Physics (who also has a small book called Gravitational Curvature )
or
P. Szekeres: A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry

B. Schutz: Geometrical Methods of Mathematical Physics
would be good as an overview... but you might find yourself looking elsewhere for more details.

I admit that I'm not so comfortable with Nakahara.You might find these useful:
http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf
https://projecteuclid.org/euclid.bams/1183539848 (article by Sachs & Wu., who also have an old book "General Relativity for Mathematicians")
http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

 

[haushofer]

I'm a Nakahara-fan :P But a text like Carroll also gives sufficient background info, I guess. Btw, I absolutely love Zee's book. It's big, but a fun read full of surprising insights and topics!

 

[ShayanJ]

I'm a Nakahara-fan :P But a text like Carroll also gives sufficient background info, I guess. Btw, I absolutely love Zee's book. It's big, but a fun read full of surprising insights and topics!

Several of reviews on amazon say that Nakahara has too many typos. Are they very bothering?(I mean the typos!)

 

[haushofer]

Several of reviews on amazon say that Nakahara has too many typos. Are they very bothering?(I mean the typos!)

Not really. I didn't have the impression is was so bad.

 

[jkl71]

I am looking to pick up one of these texts, but I don't really want to buy all three. Is there a considered favorite? Thanks in advance.

B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity

T. Frankel: The Geometry of Physics

B. Schutz: Geometrical Methods of Mathematical Physics

I like Schutz, it's pretty basic, but well done. I also think it's better oriented towards physics. I think it's a little too basic to make it you're only text, but I guess it depends on what you're looking for as an end goal. I think Frankel is good, but I found it to be a bit idiosyncratic. As a math person you might like it better though. I don't know O'Neill, so can't comment on how that compares.