Changes between Version 10 and Version 11 of u/johannjc/scratchpad

Timestamp:

10/22/13 16:01:58 (11 years ago)

Author:

Jonathan

Comment:

—

u/johannjc/scratchpad

@@ -120 +120 @@
 & = \frac{\partial_j \left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} - \partial_i\frac{(\partial_j \phi \partial_j \phi)}{8 \pi G}+\partial_i (\bar{\rho}\phi) \\
 & = \frac{\partial_j \left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} - \partial_i\left ( \frac{ \partial_j \phi \partial_j \phi}{8 \pi G} +\bar{\rho}\phi \right) \\
-& = \partial_j \frac{\left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} -  \partial_j \left ( \frac{\delta ^i_j\left(\partial_k \phi \partial_k \phi}{8 \pi G}+\bar{\rho}\phi \right) \right) \\
-& = \partial_j T_{ij} \mbox{ where } T_{ij} = \frac{\left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} -    \delta ^i_j\left(\frac{\partial_k \phi \partial_k \phi}{8 \pi G}+\bar{\rho}\phi \right) \\
+& = \partial_j \frac{\left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} -  \partial_j \left ( \delta^i_j \left ( \frac{\partial_k \phi \partial_k \phi}{8 \pi G} + \bar{\rho}\phi \right) \right )  \\
+& = \partial_j T_{ij} \mbox{ where } T_{ij} = \frac{\left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} -    \delta^i_j\left(\frac{\partial_k \phi \partial_k \phi}{8 \pi G}+\bar{\rho}\phi \right) \\
 \end{align*}
 }}}