"Einstein field equation"의 두 판 사이의 차이

2011년 11월 8일 (화) 02:27 판

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

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

\(S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x \\)

\(\kappa = {8 \pi G \over c^4} \)

@@ 3번째 줄: / 3번째 줄: @@
 * prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar
 *  relativistic matter field equation<br><math>R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}</math><br> where <math>R_{\mu \nu}</math> is the Ricci curvature tensor, <math>R</math> the Ricci scalar curvature, <math>\Lambda</math> is the [[cosmological constant]], <math>T_{\mu \nu}</math> momentum-energy tensor<br>
+<h5 style="line-height: 2em; margin: 0px;">steps to solve an Einstein equation</h5>
+*  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>
+*  find the components of the curvature tensor<br>
+*  find the components of the Einstein tensor<br>
 *   <br>
@@ 24번째 줄: / 34번째 줄: @@
 * http://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action#Derivation_of_Einstein.27s_field_equations<br>
+<h5 style="line-height: 2em; margin: 0px;">solutions example : Schwarzschild black hole</h5>
+<h5 style="line-height: 2em; margin: 0px;">solutions example :</h5>