The most rigorous relativity text is ?

[JayC]

Please don't start by saying there is no such thing as th best text or the most rigiorus text about anthing. I simply mean like we know Apostol's text fo calculus friedberg's or Hoffman's text on linear agebra Rudin's analysis text and ... what's the one about relativity? As far as I've googled I've found Relativity: Special, General, and Cosmological by Wolfgang Rindler. By the way I'm looking 4 special relativity and general relativity text or texts (it doesn't matter if both aren't covered in a singe book which by the way is the case 4 most books). Thanks in advance.

 

[Geigerclick]

MTW Gravitation.

 

[nicksauce]

Hawking & Ellis is a classic 'rigorous' text. There is also Wald, which covers more topics though at a lower level.

 

[shoehorn]

MTW Gravitation.

Not even close.

In terms of rigour, Wald is probably as close as you'll get in a book written by a physicist for physicists. There are of course heaps of monographs on the mathematical structure of relativity that present rigourous treatments of the subject at a level that mathematicians would find acceptable.

The tradeoff is usually that the more rigour included in a book, the narrower the book's subject. A good case in point is this; it's a beautiful piece of (almost) pure mathematics but isn't the sort of thing you'd read unless you had a bloody good reason.

In short, if you're interested in rigourous analyses of physical theories, there are far better areas to study than GR. Most of it's already been done; what remains is brutally difficult.

 

[Geigerclick]

Not even close.

In terms of rigour, Wald is probably as close as you'll get in a book written by a physicist for physicists. There are of course heaps of monographs on the mathematical structure of relativity that present rigourous treatments of the subject at a level that mathematicians would find acceptable.

The tradeoff is usually that the more rigour included in a book, the narrower the book's subject. A good case in point is this; it's a beautiful piece of (almost) pure mathematics but isn't the sort of thing you'd read unless you had a bloody good reason.

In short, if you're interested in rigourous analyses of physical theories, there are far better areas to study than GR. Most of it's already been done; what remains is brutally difficult.

Not even close? It seems like a good place to start for someone without a known preference. For a single book it covers a wide variety of topics related to Relativity.

 

[shoehorn]

Not even close? It seems like a good place to start for someone without a known preference. For a single book it covers a wide variety of topics related to Relativity.

All of which is true, but unrelated to the question that was asked. MTW is a wonderful book, but it doesn't even pretend to treat the subject in the rigourous manner the OP mentioned.

 

[Dickfore]

Landau Lifschitz, The Classical Theory of Fields vol.2

 

[bcrowell]

Hawking & Ellis is a classic 'rigorous' text. There is also Wald, which covers more topics though at a lower level.

Yep, and this is why I wouldn't recommend either book as an intro :-)

Hawking and Ellis isn't really meant as a general-purpose intro to GR. It is supposedly self-contained, but its real purpose is to develop the singularity theorems. Because its main topic is singularities, it starts off with an extremely detailed discussion of all the technical issues that arise when you want to deal with singularities on a manifold ... different types of differentiability and smoothness, etc., ad nauseam.

Re MTW, one of its main advantages as an intro text is its lack of rigor. I remember one passage where they say something like, "a good physical argument can never be trumped by mathematics."

As far as I've googled I've found Relativity: Special, General, and Cosmological by Wolfgang Rindler. By the way I'm looking 4 special relativity and general relativity text or texts (it doesn't matter if both aren't covered in a singe book which by the way is the case 4 most books). Thanks in advance.

This might not be a bad choice. It is in fact pretty rigorous, and unlike Wald or Hawking and Ellis, it actually might be a decent intro to relativity for someone who hasn't studied SR yet. Rindler is generally very careful about stating assumptions explicitly, not neglecting exceptional cases, etc. For someone learning SR for the first time, I especially like the fact that he includes more than one axiomatic foundation for SR. To me, a desire for rigor implies a wish to understand the foundations very clearly, and I think anyone who only encounters SR via Einstein's 1905 axiomatization is not getting that kind of deep foundational understanding. Rindler only introduces the tensor gymnastics notation, but I consider that a plus. Someone who wants to learn index-free notation, spinors, etc., can read Rindler first, then Wald or MTW for a second look.

 

[Rasalhague]

Are there significant differences between Rindler's Relativity... and the earlier (and cheaper!) Essential Relativity...?

 

[Altabeh]

Considering a rigorous intro to GR there is a book by D'Inverno which can be very fruitful when you deal with stuff at elementary to upper intermediate levels. Specially, the chapter wherein the variational methods of GR are discussed could be both instructive and thorough for rookies. But this book doesn't smell like it has the capacity to have rigor on many subjects at higher levels. For this reason, I'd like to say that D'Inverno cannot manage to stand out in the midst of other books like Wald or MTW but yet for beginners would sound like a good and reasonable choice to go with.

AB

 

[Altabeh]

Are there significant differences between Rindler's Relativity... and the earlier (and cheaper!) Essential Relativity...?

The cheaper book is really good in its content management and in fact sounds more organized from a rigorous viewpoint than the newer book. You have to add up to this the abundance of detailedness and sometimes the lack of high-level discussions of many subjects that are present in the other book. If I were to purchase one, why wouldn't I buy something that would make me end up saying "oh! this was just awesome"? In a nutshell, these books are wonderful, subtle and thought-provoking but one which was published later than the other is a little bit more advanced.

AB

 

[Landau]

Please don't start by saying there is no such thing as th best text or the most rigiorus text about anthing. I simply mean like we know Apostol's text fo calculus friedberg's or Hoffman's text on linear agebra Rudin's analysis text and ... what's the one about relativity?

You may have overlooked the fact that calculus, analysis, and linear algebra are mathematical subjects, while relativity is a theory of physics. So this is a pretty ill-posed question, or at least your examples of rigorous texts are off. A relativity text is almost by definition not rigorous in the sense of mathematical standards, since such a book would be a 'mathematical framework of relativity' text instead of a relativity text.

Among texts which take the mathematical structure of relativity seriously are Hawking-Ellis, Wald, https://www.amazon.com/dp/0486453111/?tag=pfamazon01-20, https://www.amazon.com/dp/0125267401/?tag=pfamazon01-20.

For special relativity, see this thread.

 

[redrzewski]

Take a look at Thirring, Classical Mathematical Physics vol.1. Very rigorous treatment of SR and GR.

 

[rhoparkour]

I agree with shoehorn.

Wald's book is a rigorous relativity text, but still written in a physics style. None of this "see Theorem 4.5.6" and "according to Lemma 3.5.67b" nonsense. Wald is as abstract and rigorous as possible without sacrificing the physical content of relativity.

That is the book I would recommend... Good luck finding one you like.

Note: Personally, I don't like the Misner-Thorne-Wheeler book. Specially the discussion about the Riemann tensor, ugg.

 

[Nabeshin]

Considering a rigorous intro to GR there is a book by D'Inverno which can be very fruitful when you deal with stuff at elementary to upper intermediate levels. Specially, the chapter wherein the variational methods of GR are discussed could be both instructive and thorough for rookies. But this book doesn't smell like it has the capacity to have rigor on many subjects at higher levels. For this reason, I'd like to say that D'Inverno cannot manage to stand out in the midst of other books like Wald or MTW but yet for beginners would sound like a good and reasonable choice to go with.

AB

Completely agree. If there exists such a thing as a rigorous introduction book, D'Inverno fits the bill.

 

[atyy]

http://books.google.com/books?id=k_...&resnum=1&ved=0CBcQ6AEwAA#v=onepage&q&f=false

http://www.oup.com/us/catalog/general/subject/Mathematics/AppliedMathematics/~~/dmlldz11c2EmY2k9OTc4MDE5OTIzMDcyMw==

http://www.oup.com/us/catalog/general/subject/Mathematics/AppliedMathematics/?ci=9780199215416&view=usa

 

[Daverz]

The most rigorous book, as in mathematically very careful, I know is Relativity on Curved Manifolds by de Felice and Clarke. Wald is also precise with his mathematics, sometimes unnecessarily so I think. Both are for those already somewhat familiar with GR.

I would not call Rindler rigorous in the mathematical sense, but he's very good on physical insight. Not a word I'd use for d'Inverno, either, but his book covers many topics left out of other books.

 

[George Jones]

A couple of careful books that have not yet been mentioned are

General Relativity With Applications to Astrophysics by N. Straumann
https://www.amazon.com/dp/3642060137/?tag=pfamazon01-20

An Introduction to General Relativity and Cosmology by Jerzy Plebanski and Andrzej Krasinski
https://www.amazon.com/dp/052185623X/?tag=pfamazon01-20.