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--- equations:einstein_equation [2018/03/13 11:13]
jakobadmin
+++ equations:einstein_equation [2018/05/13 09:17]
jakobadmin ↷ Links adapted because of a move operation
@@ Line 1: / Line 1: @@
-====== Einstein Equation ======
+<WRAP lag>$ G_{\mu \nu} = 8 \pi G T_{\mu \nu}$</WRAP>
-<note tip>$$ G_{\mu \nu} = 8 \pi G T_{\mu \nu}$$
+====== Einstein Equation  ======
--->Definitions#
+//see also [[theories:general_relativity]] //
-On the __right-hand side__, Newton's gravitational constant $G$, the speed of light $c$ and the stress-energy tensor $T_{\mu \nu}$.
-On the __left-hand side__, the Einstein tensor $G_{\mu \nu}$ is defined as a sum of the Ricci Tensor $R_{\mu\nu}$ and the trace of the Ricci tensor, called Ricci scalar  $R =R_{\nu}^\nu$
-\begin{equation} G_{\mu \nu} = R_{\mu\nu}-\frac{1}{2}Rg_{\mu \nu} \end{equation}
-where the Ricci Tensor $R_{\mu\nu}$ is defined in terms of the Christoffel symbols $\Gamma^\mu_{\nu \rho}$
-\begin{equation}
+<tabbox Intuitive>
-    R_{\alpha\beta} =  \partial_{\rho}{\Gamma^\rho_{\beta\alpha}} - \partial_{\beta}\Gamma^\rho_{\rho\alpha} + \Gamma^\rho_{\rho\lambda} \Gamma^\lambda_{\beta\alpha} - \Gamma^\rho_{\beta\lambda}\Gamma^\lambda_{\rho\alpha} \end{equation}
-and the Christoffel Symbols are defined in terms of the metric
-\begin{equation}
- \Gamma_{\alpha \beta \rho} =\frac12 \left(\frac{\partial g_{\alpha \beta}}{\partial x^\rho} + \frac{\partial g_{\alpha \rho}}{\partial x^\beta} - \frac{\partial g_{\beta \rho}}{\partial x^\alpha} \right) = \frac12\, \left(\partial_{\rho}g_{\alpha \beta} + \partial_{\beta}g_{\alpha \rho} - \partial_{\alpha}g_{\beta \rho}\right).  \end{equation}
-<--
-</note>
+Einstein's equation describes how spacetime gets curved through mass and energy.
-<tabbox Why is it interesting?>
+-----
-The Einstien equation is the fundamental equation of general relativity. It describes how spacetime is curved through the presence of matter and energy.
-<tabbox Layman>
   * [[http://jakobschwichtenberg.com/how-to-invent-general-relativity/|How to Invent General Relativity]] by J. Schwichtenberg
-<tabbox Student>
+<tabbox Concrete>
   * [[http://math.ucr.edu/home/baez/einstein/einstein.pdf|The Meaning of Einstein’s Equation]] by John C. Baez and Emory F. Bunn explains the Einstein equations perfectly.
@@ Line 34: / Line 21: @@
 ----
-The static limit of the Einstein equation is known as [[equations:newtons_law|Newton's law]].
+The static limit of the Einstein equation is known as [[formulas:newtons_law|Newton's law]].
-<tabbox Researcher>
+<tabbox Abstract>
 <note tip>
@@ Line 42: / Line 29: @@
 </note>
---> Common Question 1#
+<tabbox Why is it interesting?>
+The Einstein equation is the fundamental equation of general relativity. It describes how spacetime is curved through the presence of matter and energy.
-<--
---> Common Question 2#
+<tabbox Definitions>
-<--
-<tabbox Examples>
---> Example1#
+On the __right-hand side__, Newton's gravitational constant $G$, the speed of light $c$ and the stress-energy tensor $T_{\mu \nu}$.
+On the __left-hand side__, the Einstein tensor $G_{\mu \nu}$ is defined as a sum of the Ricci Tensor $R_{\mu\nu}$ and the trace of the Ricci tensor, called Ricci scalar  $R =R_{\nu}^\nu$
-<--
+\begin{equation} G_{\mu \nu} = R_{\mu\nu}-\frac{1}{2}Rg_{\mu \nu} \end{equation}
+where the Ricci Tensor $R_{\mu\nu}$ is defined in terms of the Christoffel symbols $\Gamma^\mu_{\nu \rho}$
---> Example2:#
+\begin{equation}
+    R_{\alpha\beta} =  \partial_{\rho}{\Gamma^\rho_{\beta\alpha}} - \partial_{\beta}\Gamma^\rho_{\rho\alpha} + \Gamma^\rho_{\rho\lambda} \Gamma^\lambda_{\beta\alpha} - \Gamma^\rho_{\beta\lambda}\Gamma^\lambda_{\rho\alpha} \end{equation}
+and the Christoffel Symbols are defined in terms of the metric
-<--
+\begin{equation}
+ \Gamma_{\alpha \beta \rho} =\frac12 \left(\frac{\partial g_{\alpha \beta}}{\partial x^\rho} + \frac{\partial g_{\alpha \rho}}{\partial x^\beta} - \frac{\partial g_{\beta \rho}}{\partial x^\alpha} \right) = \frac12\, \left(\partial_{\rho}g_{\alpha \beta} + \partial_{\beta}g_{\alpha \rho} - \partial_{\alpha}g_{\beta \rho}\right).  \end{equation}
-<tabbox History>
 </tabbox>

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