Can general relativity be constructed with differential forms?

[Phrak]

Can general relativity be constructed with differential forms?

 

[dextercioby]

Yes, it can. See for example Takahara's book on mathematical physics.

 

[Phrak]

Yes, it can. See for example Takahara's book on mathematical physics.

I'm coming up empty on a search for Takahara in the categories of physics or mathematics.

 

[Daverz]

I'm coming up empty on a search for Takahara in the categories of physics or mathematics.

Try Nakahara.

 

[Phrak]

Try Nakahara.

On Amazon, I found the text Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics), M. Nakahara.

To be clear, does Nakahara express general relativity in terms of differential p-forms rather than simply differential equations?

thanks, in advance.

 

[arkajad]

Can general relativity be constructed with differential forms?

It can. With bundle-valued differential forms and bundle connections. You will need to use exterior covariant derivative.

 

[raul.cuesta]

Of course you can, try N. Straumann's book: General Relativity with applications to astrophysics. In some place around chapter 2, he work with the tetrad formlism and he have an entire part of Differential Geometry.

Greetings!

 

[arkajad]

Straumann does it without fibre bundles, but on p. 111 has a footnote addressed to readers familiar with fibre bundles, so that they will recognize what he is doing using the language and the tools that are familiar to them.

 

[dextercioby]

I hope I don't mispell their names, but if you have access to Physics Reports, there's a famous review article by Eguchi, Gilkey and Hanson that I would also recommend for your attention.

 

[arkajad]

"Gravitation, gauge theories and differential geometry", Tohru Eguchi, Peter B. Gilkey, Andrew J Hanson, Physics Reports 66 no 6 (1968) 213-393. Section 3 deals with Riemannian manifolds.

 

[Esfandiar]

Yes; Here is a textbook on field theory and entirely written in the exterior calculus format :
W. Thirring, A course in Mathematical Physics, Dynamical systems and Fields (Springer)