"Einstein field equation"의 두 판 사이의 차이

2012년 1월 20일 (금) 04:13 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 \\)

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

@@ 13번째 줄: / 13번째 줄: @@
 *  find the components of the curvature tensor<br>
 *  find the components of the Einstein tensor<br>
-*   <br>
@@ 47번째 줄: / 44번째 줄: @@
-<h5 style="line-height: 2em; margin: 0px;">solutions example :</h5>
+<h5 style="line-height: 2em; margin: 0px;">solutions example : gravitational wave</h5>
+*  Einstein<br>
+*  eventually led to the graviton idea\<br>