deletions | additions       diff --git a/For_extending_to_gen.tex b/For_extending_to_gen.tex  deleted file mode 100644  index f4e4836..0000000  --- a/For_extending_to_gen.tex  +++ /dev/null 
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For extending to general spin direction, it might be of use to  re-express the conformal factor in terms of the vector $\vec{a}$:  &=& (R^2 + a^2) + \frac{2 M a^2 R \sin^2{\theta}}{R^2 + a^2 \cos^2{\theta}} = (R^2 + a^2) + \frac{2 M R |\hatXvec{n}{a}|^2}{R^2 + (\hatDvec{n}{a})^2}\\  &=& (R^2 + a^2) + \frac{2 M R |\vecXvec{x}{a}|^2}{R^2 r^2 + (\vecdot{x}{a})^2} = (R^2 + a^2) + \frac{2 M R [r^2 a^2 - (\vecdot{x}{a})^2] }{R^2 r^2 + (\vecdot{x}{a})^2}  Now we can take radial derivatives more easily:  &= & 2 R \partial_r R + 2 M \frac{\partial_r R [r^2 a^2 - (\vecdot{x}{a})^2] + R [2 a^2 r - 2 (\vecdot{x}{a}) (\hatDvec{n}{a}) }{R^2 r^2 + (\vecdot{x}{a})^2} \\  && - \frac{2 M R [r^2 a^2 - (\vecdot{x}{a})^2] }{[R^2 r^2 + (\vecdot{x}{a})^2]^2} \left( 2 R r^2 \partial_r R + 2 R^2 r + 2 (\vecdot{x}{a}) (\hatDvec{n}{a}) \right)  diff --git a/layout.md b/layout.md  index 00f977c..4d7d9d7 100644  --- a/layout.md  +++ b/layout.md 
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The_determinant_of_t.tex  brace_tildegamma_i_j_.tex  which_leads_to_the.tex  For_extending_to_gen.tex  We_can_push_the.tex  eqnarray*_psi_04r___frac710560.tex  brace_g_mu_nu_.tex