Changes between Version 9 and Version 10 of u/johannjc/scratchpad


Ignore:
Timestamp:
10/22/13 15:54:35 (11 years ago)
Author:
Jonathan
Comment:

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  • u/johannjc/scratchpad

    v9 v10  
    119119& = \frac{\partial_j \left ( \partial_j \phi \partial_i \phi \right) - (\partial_j \phi) \partial_i (\partial_j \phi )}{4 \pi G}+\partial_i (\bar{\rho}\phi) \\
    120120& = \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) \\
    121 & = \frac{\partial_j \left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} - \partial_i\frac{ \left (\partial_j \phi \partial_j \phi}{8 \pi G} +\bar{\rho}\phi \right) \\
    122 & = \partial_j \frac{\left ( \partial_j \phi \partial_i \phi \right)}{4 \pi G} -  \partial_j \frac{\left ( \delta ^i_j\left(\partial_k \phi \partial_k \phi}{8 \pi G}+\bar{\rho}\phi \right) \right) \\
     121& = \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) \\
     122& = \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) \\
    123123& = \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) \\
    124124\end{align*}