Einstein field equation
http://bomber0.myid.net/ (토론)님의 2011년 11월 8일 (화) 02:27 판
introduction
- prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar
- relativistic matter field equation
\(R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\)
where \(R_{\mu \nu}\) is the Ricci curvature tensor, \(R\) the Ricci scalar curvature, \(\Lambda\) is the cosmological constant, \(T_{\mu \nu}\) momentum-energy tensor
steps to solve an Einstein equation
- consider a metric, for example
\(ds^2=-dt^2+e^{2b(t,r)}dr^2+R(t,r)d\phi^2\)
where b, R are unknown functions - find the components of the curvature tensor
- find the components of the Einstein tensor
-
Einstein-Hilbert action
\(S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x \\)
\(\kappa = {8 \pi G \over c^4} \)
equation of motion
solutions example : Schwarzschild black hole
solutions example :
history
- cosmological constant
- differential geometry and topology
- Yang-Mills Theory(Non-Abelian gauge theory)
- string theory and Einstein equations
encyclopedia
-
- [1]http://en.wikipedia.org/wiki/Einstein_field_equations
- http://en.wikipedia.org/wiki/Riemann_curvature_tensor
- http://en.wikipedia.org/wiki/Ricci_curvature
- http://en.wikipedia.org/wiki/Scalar_curvature[2]
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
expositions
articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field