deletions | additions       diff --git a/We_can_calculate_the.tex b/We_can_calculate_the.tex  deleted file mode 100644  index 8a8938c..0000000  --- a/We_can_calculate_the.tex  +++ /dev/null 
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We can calculate the expansion $\Theta$ of outgoing ($l^a$) and  ingoing ($n^a$) null normals to spherical surfaces for these  coordinates. Here, the spatial unit normal is $s^i = \frac{x^i}{R}$,  and  & = & \partial_i \frac{x^i}{R} + \sqrt{\frac{2M}{R^3}}\left( \delta_{i j} - \frac{3x_ix_j}{2R^2} \right) \left( \frac{x^i}{R} \frac{x^j}{R} - \delta^{i j} \right)\\  & = & \frac{2}{R} - 2 \sqrt{\frac{2 M}{R^3}},  which vanishes at $R = 2 M$, as we would expect. Similarly,  diff --git a/layout.md b/layout.md  index 2543080..5c1b3ac 100644  --- a/layout.md  +++ b/layout.md 
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In_PainleveGullstran.tex  This_decomposes_into.tex  brace_Theta_n__.tex  We_can_calculate_the.tex  brace_ds2__left.tex  For_the_shift_Combine_the_mixedfor.tex  subsectionKerrSchild.tex