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Tensor calculus for general relativity 
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#1
Mar1810, 11:45 AM

P: 1

I'm taking a course on relativity, both special and general. According to my college, I have the required mathematical background (vector analysis, electromagnetics (though I can't recall more than a cursory glance at tensors) etc) to make sense of it. Special relativity I can handle, and I think I understand the general concepts of GR fairly well, but how to actually do the math eludes me.
The book I have is TaPei Cheng's Relativity, Gravitation and Cosmology. It does an OK job of explaining the theory, but it tends to not do the calculations, instead calling them 'straight forward'. Math has, sadly, never came that naturally to me, and I don't follow. So what I need would be a guide to the mathematical framework, one that spells it all out explicitly. Does anyone have any recommendations? 


#2
Mar1810, 02:11 PM

P: 2,179

Misner, Thorne, and Wheeler is the classic reference on GR, and it explains tensor calculus from several different viewpoints, so it might be a good reference.



#3
Mar1810, 07:23 PM

P: 5,632

Some online sopurces....
Some Caltech notes: http://nedwww.ipac.caltech.edu/level..._contents.html And from Benjamin Crowell of this forum: http://www.lightandmatter.com/html_b...ch04/ch04.html And from John Baez, http://math.ucr.edu/home/baez/gr/gr.html And from Hofstra, http://people.hofstra.edu/Stefan_Wan...f_geom/tc.html And from mathpages, around 5.2: http://www.mathpages.com/rr/s502/502.htm Good luck..I collected some references but have not studied them due to time constraints so I can't recommend one over another. 


#4
Mar1910, 05:11 PM

P: 1,402

Tensor calculus for general relativity
Sean Carroll's Lecture Notes on General Relativity can also be found here, along with a condensed version and some further resources.
http://www.pma.caltech.edu/Courses/ph136/yr2008/ Kip Thorne & Roger Blandford: Applications of Classical Phyisics http://www.pma.caltech.edu/Courses/ph136/yr2008/ Kip Thorne also has a series of video lectures online about gravitational waves, which include an introduction to tensor analysis. http://elmer.tapir.caltech.edu/ph237...eOutlineA.html I found the following book, online in PDF format, helpful in getting a handle on some of the basic mathematical concepts relating to tensors: vector spaces, dual spaces, etc. Ray M. Bowen and C. C. Wang: Introduction to Vectors and Tensors, Vol 1: Linear and Multilinear Algebra http://repository.tamu.edu/handle/1969.1/2502 Ray M. Bowen and C. C. Wang: Introduction to Vectors and Tensors, Vol 2: Vector and Tensor Analysis http://repository.tamu.edu/handle/1969.1/3609 Part two of this series of video lectures from MIT has an introduction to tensors, from the second half of lecture 15 onwards, although it only deals with orthonormal coordinate systems. http://ocw.mit.edu/OcwWeb/Materials...Home/index.htm 


#5
Mar2010, 10:44 PM

P: 97

Are you a Chinese?There is a series books on Differential and General Relativity written by 梁灿彬,it's nice!



#6
May1610, 01:38 AM

P: 134




#7
Jun2910, 10:04 AM

P: 3

There is a book which talks about the tools for practical computation,
"A relativist's toolkit: the mathematics of blackhole mechanics " I am now reading it, and I think it is very helpful~ 


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