"Einstein field equation"의 두 판 사이의 차이
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steps to solve an Einstein equation==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar | * prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar | ||
| 8번째 줄: | 8번째 줄: | ||
| − | <h5 style="line-height: 2em; margin: 0px;">steps to solve an Einstein equation | + | <h5 style="line-height: 2em; margin: 0px;">steps to solve an Einstein equation== |
* consider a metric, for example<br><math>ds^2=-dt^2+e^{2b(t,r)}dr^2+R(t,r)d\phi^2</math><br> where b, R are unknown functions<br> | * consider a metric, for example<br><math>ds^2=-dt^2+e^{2b(t,r)}dr^2+R(t,r)d\phi^2</math><br> where b, R are unknown functions<br> | ||
| 18번째 줄: | 18번째 줄: | ||
| − | <h5 style="line-height: 2em; margin: 0px;">Einstein-Hilbert action | + | <h5 style="line-height: 2em; margin: 0px;">Einstein-Hilbert action== |
* Einstein-Hilbert action<br><math>S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x \</math><br><math>\kappa = {8 \pi G \over c^4} </math><br> | * Einstein-Hilbert action<br><math>S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x \</math><br><math>\kappa = {8 \pi G \over c^4} </math><br> | ||
| 26번째 줄: | 26번째 줄: | ||
| − | <h5 style="line-height: 2em; margin: 0px;">equation of motion | + | <h5 style="line-height: 2em; margin: 0px;">equation of motion== |
* http://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action#Derivation_of_Einstein.27s_field_equations<br> | * http://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action#Derivation_of_Einstein.27s_field_equations<br> | ||
| 34번째 줄: | 34번째 줄: | ||
| − | <h5 style="line-height: 2em; margin: 0px;">solutions example : Schwarzschild black hole | + | <h5 style="line-height: 2em; margin: 0px;">solutions example : Schwarzschild black hole== |
| 42번째 줄: | 42번째 줄: | ||
| − | <h5 style="line-height: 2em; margin: 0px;">solutions example : gravitational wave | + | <h5 style="line-height: 2em; margin: 0px;">solutions example : gravitational wave== |
* Einstein<br> | * Einstein<br> | ||
| 51번째 줄: | 51번째 줄: | ||
| − | ==history | + | ==history== |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 59번째 줄: | 59번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[cosmological constant]] | * [[cosmological constant]] | ||
| 70번째 줄: | 70번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia== |
* [http://en.wikipedia.org/wiki/Einstein_field_equations ]http://en.wikipedia.org/wiki/Einstein_field_equations | * [http://en.wikipedia.org/wiki/Einstein_field_equations ]http://en.wikipedia.org/wiki/Einstein_field_equations | ||
2012년 10월 28일 (일) 15:26 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==
- 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 : gravitational wave==
- Einstein
- eventually led to the graviton idea\
history
- cosmological constant
- differential geometry and topology
- Yang-Mills Theory(Non-Abelian gauge theory)
- string theory and Einstein equations
encyclopedia==
\(ds^2=-dt^2+e^{2b(t,r)}dr^2+R(t,r)d\phi^2\)
where b, R are unknown functions
- Einstein-Hilbert action
\(S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x \\)
\(\kappa = {8 \pi G \over c^4} \)
- Einstein
- eventually led to the graviton idea\