"Einstein field equation"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5 (.*)">” 문자열을 “==” 문자열로) |
||
| 8번째 줄: | 8번째 줄: | ||
| − | + | ==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: | ||
| − | + | ==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: | ||
| − | + | ==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: | ||
| − | + | ==solutions example : Schwarzschild black hole== | |
| 42번째 줄: | 42번째 줄: | ||
| − | + | ==solutions example : gravitational wave== | |
* Einstein<br> | * Einstein<br> | ||
| 70번째 줄: | 70번째 줄: | ||
| − | + | ==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) 17:16 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