deletions | additions       diff --git a/subsectionKerrSchild.tex b/subsectionKerrSchild.tex  index 5b8e7c4..397a4c5 100644  --- a/subsectionKerrSchild.tex  +++ b/subsectionKerrSchild.tex 
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\begin{array*}  g_{\mu \nu} &= \eta_{\mu \nu} + 2 H \ell_{\mu} \ell_{\nu},\\  \Rightarrow g^{\mu \nu} &= \eta^{\mu \nu} - 2 H \ell^{\mu} \ell^{\nu},\\  \alpha &= \frac{1}{\sqrt{1 + 2 H \ell_0^2}},\\   \beta_i &= 2 H \ell_0 \ell_i,\\   \beta^i &= \frac{2 H \ell_0 \ell^i}{1 + 2 H \ell_0^2},\\   \gamma_{i j} &= \eta_{i j} + 2H \ell_i \ell_j,\\   \gamma^{i j} &= \eta^{i j} - \frac{2H}{1 + 2 H \ell_0^2} \ell^i \ell^j,\\   \Rightarrow \gamma_{i j,k} &= 2 \left[ H_{,k} \ell_i \ell_j + H \ell_{i,k} \ell_j + H \ell_i \ell_{j,k} \right], \\   K_{i j} &= \alpha \left[ \ell_i H_{,j} + \ell_j H_{,i} + H \ell_{i,j} + H \ell_{j,i} + 2 H ^2 \left( \ell_i \ell_m \ell_{j,m} + \ell_j \ell_m \ell_{i,m} \right) + 2 H \ell_i \ell_j \ell_m H_{,m} \right].   \end{array*}  This agrees with the formula presented in eqn (35) of \citet{Yo:2002bm}.