${\rho} = {{{{x}^{2}} + {{y}^{2}} + {{z}^{2}}} - {{a}^{2}}}$
${\partial_ {{x}}\left( \rho\right)} = {{{2}} {{x}}}$
${\partial_ {{y}}\left( \rho\right)} = {{{2}} {{y}}}$
${\partial_ {{z}}\left( \rho\right)} = {{{2}} {{z}}}$

${{r}^{2}} = {{{\frac{1}{2}}} {{\left({{\rho} + {\sqrt{{{\rho}^{2}} + {{{4}} {{{a}^{2}}} {{{z}^{2}}}}}}}\right)}}}$
${\partial_ {{x}}\left( r\right)} = {\frac{{{x}} {{\left({{1} + {{{\rho}} \cdot {{\frac{1}{\sqrt{{{\rho}^{2}} + {{{4}} {{{a}^{2}}} {{{z}^{2}}}}}}}}}}\right)}}}{{{2}} {{r}}}}$
${\partial_ {{y}}\left( r\right)} = {\frac{{{y}} {{\left({{1} + {{{\rho}} \cdot {{\frac{1}{\sqrt{{{\rho}^{2}} + {{{4}} {{{a}^{2}}} {{{z}^{2}}}}}}}}}}\right)}}}{{{2}} {{r}}}}$
${\partial_ {{z}}\left( r\right)} = {\frac{{{z}} {{\left({{1} + {{{\rho}} \cdot {{\frac{1}{\sqrt{{{\rho}^{2}} + {{{4}} {{{a}^{2}}} {{{z}^{2}}}}}}}}} + {{{2}} {{{a}^{2}}} {{\frac{1}{\sqrt{{{\rho}^{2}} + {{{4}} {{{a}^{2}}} {{{z}^{2}}}}}}}}}}\right)}}}{{{2}} {{r}}}}$

${H} = {\frac{{{{r}} {{M}}} - {{\frac{1}{2}} {{Q}^{2}}}}{{{r}^{2}} + {\frac{{{{a}^{2}}} {{{z}^{2}}}}{{r}^{2}}}}}$
${\partial_ {{x}}\left( H\right)} = {\frac{{{\partial_ {{x}}\left( r\right)}} {{\left({{{{{3}} {{M}} {{{a}^{2}}} {{{r}^{2}}} {{{z}^{2}}}} - {{{M}} {{{r}^{6}}}}} + {{{{{Q}^{2}}} {{{r}^{5}}}} - {{{r}} {{{Q}^{2}}} {{{a}^{2}}} {{{z}^{2}}}}}}\right)}}}{{{{{a}^{4}}} {{{z}^{4}}}} + {{{2}} {{{a}^{2}}} {{{r}^{4}}} {{{z}^{2}}}} + {{r}^{8}}}}$
${\partial_ {{y}}\left( H\right)} = {\frac{{{\partial_ {{y}}\left( r\right)}} {{\left({{{{{3}} {{M}} {{{a}^{2}}} {{{r}^{2}}} {{{z}^{2}}}} - {{{M}} {{{r}^{6}}}}} + {{{{{Q}^{2}}} {{{r}^{5}}}} - {{{r}} {{{Q}^{2}}} {{{a}^{2}}} {{{z}^{2}}}}}}\right)}}}{{{{{a}^{4}}} {{{z}^{4}}}} + {{{2}} {{{a}^{2}}} {{{r}^{4}}} {{{z}^{2}}}} + {{r}^{8}}}}$
${\partial_ {{z}}\left( H\right)} = {\frac{{{{{{3}} {{M}} {{{a}^{2}}} {{{r}^{2}}} {{{z}^{2}}} {{\partial_ {{z}}\left( r\right)}}} - {{{M}} {{{r}^{6}}} {{\partial_ {{z}}\left( r\right)}}}} - {{{2}} {{M}} {{z}} {{{a}^{2}}} {{{r}^{3}}}}} + {{{{{Q}^{2}}} {{{r}^{5}}} {{\partial_ {{z}}\left( r\right)}}} - {{{r}} {{{Q}^{2}}} {{{a}^{2}}} {{{z}^{2}}} {{\partial_ {{z}}\left( r\right)}}}} + {{{z}} {{{Q}^{2}}} {{{a}^{2}}} {{{r}^{2}}}}}{{{{{a}^{4}}} {{{z}^{4}}}} + {{{2}} {{{a}^{2}}} {{{r}^{4}}} {{{z}^{2}}}} + {{r}^{8}}}}$

${{{ \eta} _u} _v} = {\overset{u\downarrow v\rightarrow}{\left[ \begin{matrix} -{1} & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix} \right]}}$
${{{ \eta} ^u} ^v} = {\overset{u\downarrow v\rightarrow}{\left[ \begin{matrix} -{1} & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix} \right]}}$
${{ l} _t} = {1}$
${{ l} _x} = {\frac{{{{r}} {{x}}} + {{{a}} {{y}}}}{{{r}^{2}} + {{a}^{2}}}}$
${{ l} _y} = {\frac{{{{r}} {{y}}} - {{{a}} {{x}}}}{{{r}^{2}} + {{a}^{2}}}}$
${{ l} _z} = {{\frac{1}{r}} {z}}$

${0} = {\frac{{-{{{x}} {{{r}^{2}}} {{\partial_ {{x}}\left( r\right)}}}} + {{{x}} {{{a}^{2}}} {{\partial_ {{x}}\left( r\right)}}} + {{r}^{3}} + {{{{r}} {{{a}^{2}}}} - {{{2}} {{a}} {{r}} {{y}} {{\partial_ {{x}}\left( r\right)}}}}}{{{{2}} {{{a}^{2}}} {{{r}^{2}}}} + {{r}^{4}} + {{a}^{4}}}}$
${0} = {\frac{{-{{{x}} {{{r}^{2}}} {{\partial_ {{y}}\left( r\right)}}}} + {{{x}} {{{a}^{2}}} {{\partial_ {{y}}\left( r\right)}}} + {{{a}} {{{r}^{2}}}} + {{{a}^{3}} - {{{2}} {{a}} {{r}} {{y}} {{\partial_ {{y}}\left( r\right)}}}}}{{{{2}} {{{a}^{2}}} {{{r}^{2}}}} + {{r}^{4}} + {{a}^{4}}}}$
${0} = {\frac{{{\partial_ {{z}}\left( r\right)}} {{\left({{-{{{2}} {{a}} {{r}} {{y}}}} + {{{{x}} {{{a}^{2}}}} - {{{x}} {{{r}^{2}}}}}}\right)}}}{{{{2}} {{{a}^{2}}} {{{r}^{2}}}} + {{r}^{4}} + {{a}^{4}}}}$
${0} = {\frac{{-{{{y}} {{{r}^{2}}} {{\partial_ {{x}}\left( r\right)}}}} + {{{{{y}} {{{a}^{2}}} {{\partial_ {{x}}\left( r\right)}}} - {{{a}} {{{r}^{2}}}}} - {{a}^{3}}} + {{{2}} {{a}} {{r}} {{x}} {{\partial_ {{x}}\left( r\right)}}}}{{{{2}} {{{a}^{2}}} {{{r}^{2}}}} + {{r}^{4}} + {{a}^{4}}}}$
${0} = {\frac{{-{{{y}} {{{r}^{2}}} {{\partial_ {{y}}\left( r\right)}}}} + {{{y}} {{{a}^{2}}} {{\partial_ {{y}}\left( r\right)}}} + {{r}^{3}} + {{{r}} {{{a}^{2}}}} + {{{2}} {{a}} {{r}} {{x}} {{\partial_ {{y}}\left( r\right)}}}}{{{{2}} {{{a}^{2}}} {{{r}^{2}}}} + {{r}^{4}} + {{a}^{4}}}}$
${0} = {\frac{{{\partial_ {{z}}\left( r\right)}} {{\left({{{{2}} {{a}} {{r}} {{x}}} + {{{{y}} {{{a}^{2}}}} - {{{y}} {{{r}^{2}}}}}}\right)}}}{{{{2}} {{{a}^{2}}} {{{r}^{2}}}} + {{r}^{4}} + {{a}^{4}}}}$
${0} = {-{\frac{{{z}} {{\partial_ {{x}}\left( r\right)}}}{{r}^{2}}}}$
${0} = {-{\frac{{{z}} {{\partial_ {{y}}\left( r\right)}}}{{r}^{2}}}}$
${0} = {\frac{{r} - {{{z}} {{\partial_ {{z}}\left( r\right)}}}}{{r}^{2}}}$
${{ l} _u} = {\overset{u\downarrow}{\left[ \begin{matrix} 1 \\ {l_x} \\ {l_y} \\ {l_z}\end{matrix} \right]}}$
${{ l} ^u} = {{{{ l} _v}} {{{{ \eta} ^u} ^v}}}$
${{ l} ^u} = {\overset{u\downarrow}{\left[ \begin{matrix} -{1} \\ {l_x} \\ {l_y} \\ {l_z}\end{matrix} \right]}}$
${{{ g} _u} _v} = {{{{ \eta} _u} _v} + {{{2}} {{H}} {{{ l} _u}} {{{ l} _v}}}}$
${{{ g} _u} _v} = {\overset{u\downarrow v\rightarrow}{\left[ \begin{matrix} {-{1}} + {{{2}} {{H}}} & {{2}} {{H}} {{{l_x}}} & {{2}} {{H}} {{{l_y}}} & {{2}} {{H}} {{{l_z}}} \\ {{2}} {{H}} {{{l_x}}} & {1} + {{{2}} {{H}} {{{{l_x}}^{2}}}} & {{2}} {{H}} {{{l_x}}} \cdot {{{l_y}}} & {{2}} {{H}} {{{l_x}}} \cdot {{{l_z}}} \\ {{2}} {{H}} {{{l_y}}} & {{2}} {{H}} {{{l_x}}} \cdot {{{l_y}}} & {1} + {{{2}} {{H}} {{{{l_y}}^{2}}}} & {{2}} {{H}} {{{l_y}}} \cdot {{{l_z}}} \\ {{2}} {{H}} {{{l_z}}} & {{2}} {{H}} {{{l_x}}} \cdot {{{l_z}}} & {{2}} {{H}} {{{l_y}}} \cdot {{{l_z}}} & {1} + {{{2}} {{H}} {{{{l_z}}^{2}}}}\end{matrix} \right]}}$
${{{ g} ^u} ^v} = {{{{ \eta} ^u} ^v} - {{{2}} {{H}} {{{ l} ^u}} {{{ l} ^v}}}}$
${{{ g} ^u} ^v} = {\overset{u\downarrow v\rightarrow}{\left[ \begin{matrix} -{\left({{1} + {{{2}} {{H}}}}\right)} & {{2}} {{H}} {{{l_x}}} & {{2}} {{H}} {{{l_y}}} & {{2}} {{H}} {{{l_z}}} \\ {{2}} {{H}} {{{l_x}}} & {1} - {{{2}} {{H}} {{{{l_x}}^{2}}}} & -{{{2}} {{H}} {{{l_x}}} \cdot {{{l_y}}}} & -{{{2}} {{H}} {{{l_x}}} \cdot {{{l_z}}}} \\ {{2}} {{H}} {{{l_y}}} & -{{{2}} {{H}} {{{l_x}}} \cdot {{{l_y}}}} & {1} - {{{2}} {{H}} {{{{l_y}}^{2}}}} & -{{{2}} {{H}} {{{l_y}}} \cdot {{{l_z}}}} \\ {{2}} {{H}} {{{l_z}}} & -{{{2}} {{H}} {{{l_x}}} \cdot {{{l_z}}}} & -{{{2}} {{H}} {{{l_y}}} \cdot {{{l_z}}}} & {1} - {{{2}} {{H}} {{{{l_z}}^{2}}}}\end{matrix} \right]}}$
${{{{ g} _u} _v} _{,w}} = {\overset{u\downarrow[{v\downarrow w\rightarrow}]}{\left[ \begin{matrix} \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} 0 & {{2}} {{\partial_ {{x}}\left( H\right)}} & {{2}} {{\partial_ {{y}}\left( H\right)}} & {{2}} {{\partial_ {{z}}\left( H\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}}\end{matrix} \right]} \\ \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} 0 & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}}\end{matrix} \right]} \\ \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} 0 & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}}\end{matrix} \right]} \\ \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} 0 & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{\left({{{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{\left({{{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ 0 & {{2}} {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{2}} {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{2}} {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}}\end{matrix} \right]}\end{matrix} \right]}}$
${{{{ \Gamma} _a} _b} _c} = {\overset{a\downarrow[{b\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} 0 & \partial_ {{x}}\left( H\right) & \partial_ {{y}}\left( H\right) & \partial_ {{z}}\left( H\right) \\ \partial_ {{x}}\left( H\right) & {{2}} {{\left({{{{H}} {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} \\ \partial_ {{y}}\left( H\right) & {{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {{2}} {{\left({{{{H}} {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} \\ \partial_ {{z}}\left( H\right) & {{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} & {{2}} {{\left({{{{H}} {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}}\end{matrix} \right]} \\ \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} -{\partial_ {{x}}\left( H\right)} & 0 & {{{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}} & {{{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}} \\ 0 & {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ {{{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}} & {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{2}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{{{l_y}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} & {{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} + {{{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}} \\ {{{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}} & {{{l_x}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} & {{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} + {{{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}} & {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{2}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{{l_z}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}}\end{matrix} \right]} \\ \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} -{\partial_ {{y}}\left( H\right)} & {-{{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & 0 & {{{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}} \\ {-{{{H}} {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{{l_x}}} \cdot {{\partial_ {{y}}\left( H\right)}}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {-{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} - {{{{{l_x}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{2}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} \\ 0 & {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ {{{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}} & {{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {{{l_y}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} & {{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{2}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{{{l_z}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}}\end{matrix} \right]} \\ \overset{v\downarrow w\rightarrow}{\left[ \begin{matrix} -{\partial_ {{z}}\left( H\right)} & {-{{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {-{{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} & 0 \\ {-{{{H}} {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{{l_x}}} \cdot {{\partial_ {{z}}\left( H\right)}}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {-{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} - {{{{{l_x}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{2}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {-{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} \\ {-{{{H}} {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} & {-{{{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{z}}\left( H\right)}}}} + {{{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} + {{{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} & {-{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} - {{{{{l_y}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{2}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} & {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} \\ 0 & {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}}}\right)}} & {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}}}\right)}} & {{{l_z}}} \cdot {{\left({{{{2}} {{H}} {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}}\end{matrix} \right]}\end{matrix} \right]}}$
${{{ \Gamma} _a} = {{{{{{ \Gamma} _a} _b} _c}} {{{{ g} ^b} ^c}}}} = {\overset{a\downarrow}{\left[ \begin{matrix} {{2}} {{\left({{{{-{{{2}} {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{x}}\left( {l_x}\right)}}}} - {{{2}} {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{y}}\left( {l_y}\right)}}}} - {{{2}} {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{z}}\left( {l_z}\right)}}}} + {{{H}} {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{H}} {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{H}} {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}} - {{{2}} {{H}} {{{{l_x}}^{3}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_x}}} \cdot {{{{l_y}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_x}}} \cdot {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{2}} {{H}} {{{{l_y}}^{3}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{2}} {{H}} {{{l_y}}} \cdot {{{{l_x}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_y}}} \cdot {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{2}} {{H}} {{{{l_z}}^{3}}} {{\partial_ {{z}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_z}}} \cdot {{{{l_x}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_z}}} \cdot {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{{{{{{l_x}}} \cdot {{\partial_ {{x}}\left( H\right)}}} - {{{2}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}}} - {{{2}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}}} - {{{2}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}}} - {{{2}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{2}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}}} - {{{2}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}}}\right)}} \\ {\partial_ {{x}}\left( H\right)} + {{{2}} {{H}} {{\partial_ {{x}}\left( H\right)}}} + {{{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{4}} {{H}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{4}} {{H}} {{{{l_y}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} + {{{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{4}} {{H}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{H}} {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} + {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} + {{{{{{{{{{{l_x}}^{2}}} {{\partial_ {{x}}\left( H\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_x}}^{3}}} {{\partial_ {{x}}\left( {l_x}\right)}}}} - {{{2}} {{H}} {{{{l_x}}^{4}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{8}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}}} - {{{4}} {{H}} {{{l_y}}} \cdot {{{{l_x}}^{3}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{8}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}}} - {{{4}} {{H}} {{{l_z}}} \cdot {{{{l_x}}^{3}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} - {{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{y}}\left( {l_y}\right)}}}} + {{{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_y}}^{3}}} {{\partial_ {{y}}\left( {l_x}\right)}}}} - {{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{4}} {{{H}^{2}}} {{{{l_y}}^{3}}} {{\partial_ {{x}}\left( {l_y}\right)}}} + {{{{{2}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{{l_y}}^{3}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{{{l_y}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} + {{{{{{2}} {{H}} {{{{l_y}}^{4}}} {{\partial_ {{x}}\left( H\right)}}} - {{{4}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}}} - {{{4}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}}} - {{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{4}} {{H}} {{{{l_y}}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( H\right)}}} + {{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} - {{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{z}}\left( {l_z}\right)}}}} + {{{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_z}}^{3}}} {{\partial_ {{z}}\left( {l_x}\right)}}}} - {{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{4}} {{{H}^{2}}} {{{{l_z}}^{3}}} {{\partial_ {{x}}\left( {l_z}\right)}}} + {{{{{2}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{{l_z}}^{3}}} {{\partial_ {{z}}\left( H\right)}}}} - {{{{{l_z}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} + {{{2}} {{H}} {{{{l_z}}^{4}}} {{\partial_ {{x}}\left( H\right)}}} \\ {\partial_ {{y}}\left( H\right)} + {{{{2}} {{H}} {{\partial_ {{y}}\left( H\right)}}} - {{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{4}} {{H}} {{{{l_x}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{4}} {{H}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} + {{{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{{4}} {{H}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{H}} {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{y}}\left( {l_x}\right)}}}} + {{{4}} {{{H}^{2}}} {{{{l_x}}^{3}}} {{\partial_ {{y}}\left( {l_x}\right)}}} + {{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_y}\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_x}}^{3}}} {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} - {{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{x}}\left( {l_x}\right)}}}} - {{{{{l_x}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{2}} {{H}} {{{{l_x}}^{4}}} {{\partial_ {{y}}\left( H\right)}}} + {{{{{{{2}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{\partial_ {{x}}\left( H\right)}}} - {{{4}} {{H}} {{{l_y}}} \cdot {{{{l_x}}^{3}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{8}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{{l_y}}^{3}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{4}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}}} - {{{4}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}} - {{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}}} - {{{4}} {{H}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{{{l_x}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{{4}} {{H}} {{{{l_x}}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( H\right)}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} + {{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} + {{{{{{{{{l_y}}^{2}}} {{\partial_ {{y}}\left( H\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_y}}^{3}}} {{\partial_ {{y}}\left( {l_y}\right)}}}} - {{{2}} {{H}} {{{{l_y}}^{4}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{8}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}}} - {{{4}} {{H}} {{{l_z}}} \cdot {{{{l_y}}^{3}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} - {{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{z}}\left( {l_z}\right)}}}} + {{{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_z}}^{3}}} {{\partial_ {{z}}\left( {l_y}\right)}}}} - {{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{4}} {{{H}^{2}}} {{{{l_z}}^{3}}} {{\partial_ {{y}}\left( {l_z}\right)}}} + {{{{{2}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{H}} {{{l_y}}} \cdot {{{{l_z}}^{3}}} {{\partial_ {{z}}\left( H\right)}}}} - {{{{{l_z}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{2}} {{H}} {{{{l_z}}^{4}}} {{\partial_ {{y}}\left( H\right)}}} \\ {\partial_ {{z}}\left( H\right)} + {{{{2}} {{H}} {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{4}} {{H}} {{{{l_x}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{{4}} {{H}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} - {{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{4}} {{H}} {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{{4}} {{H}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{z}}\left( {l_x}\right)}}}} + {{{4}} {{{H}^{2}}} {{{{l_x}}^{3}}} {{\partial_ {{z}}\left( {l_x}\right)}}} + {{{{2}} {{H}} {{{l_x}}} \cdot {{\partial_ {{x}}\left( {l_z}\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_x}}^{3}}} {{\partial_ {{x}}\left( {l_z}\right)}}}} + {{{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{x}}\left( {l_x}\right)}}} - {{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{x}}\left( {l_x}\right)}}}} - {{{{{l_x}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{2}} {{H}} {{{{l_x}}^{4}}} {{\partial_ {{z}}\left( H\right)}}} + {{{{2}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{\partial_ {{x}}\left( H\right)}}} - {{{4}} {{H}} {{{l_z}}} \cdot {{{{l_x}}^{3}}} {{\partial_ {{x}}\left( H\right)}}}} + {{{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{z}}\left( {l_y}\right)}}} - {{{4}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_x}}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( {l_x}\right)}}} - {{{4}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}}} - {{{4}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{y}}\left( {l_x}\right)}}}} - {{{4}} {{{l_x}}} \cdot {{{l_y}}} \cdot {{{l_z}}} \cdot {{{H}^{2}}} {{\partial_ {{x}}\left( {l_y}\right)}}}} + {{{{{{{{4}} {{H}} {{{{l_x}}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{H}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{{{l_x}}^{2}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{l_z}}} \cdot {{{{l_y}}^{2}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{8}} {{{l_x}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{x}}\left( {l_z}\right)}}}} - {{{4}} {{H}} {{{l_x}}} \cdot {{{{l_z}}^{3}}} {{\partial_ {{x}}\left( H\right)}}}} - {{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{z}}\left( {l_y}\right)}}}} + {{{4}} {{{H}^{2}}} {{{{l_y}}^{3}}} {{\partial_ {{z}}\left( {l_y}\right)}}} + {{{{2}} {{H}} {{{l_y}}} \cdot {{\partial_ {{y}}\left( {l_z}\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_y}}^{3}}} {{\partial_ {{y}}\left( {l_z}\right)}}}} + {{{{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{y}}\left( {l_y}\right)}}} - {{{4}} {{{l_z}}} \cdot {{{H}^{2}}} {{{{l_y}}^{2}}} {{\partial_ {{y}}\left( {l_y}\right)}}}} - {{{{{l_y}}^{2}}} {{\partial_ {{z}}\left( H\right)}}}} + {{{2}} {{H}} {{{{l_y}}^{4}}} {{\partial_ {{z}}\left( H\right)}}} + {{{{{{2}} {{{l_y}}} \cdot {{{l_z}}} \cdot {{\partial_ {{y}}\left( H\right)}}} - {{{4}} {{H}} {{{l_z}}} \cdot {{{{l_y}}^{3}}} {{\partial_ {{y}}\left( H\right)}}}} - {{{8}} {{{l_y}}} \cdot {{{H}^{2}}} {{{{l_z}}^{2}}} {{\partial_ {{y}}\left( {l_z}\right)}}}} - {{{4}} {{H}} {{{l_y}}} \cdot {{{{l_z}}^{3}}} {{\partial_ {{y}}\left( H\right)}}}} + {{{2}} {{H}} {{{l_z}}} \cdot {{\partial_ {{z}}\left( {l_z}\right)}}} + {{{{{{{l_z}}^{2}}} {{\partial_ {{z}}\left( H\right)}}} - {{{4}} {{{H}^{2}}} {{{{l_z}}^{3}}} {{\partial_ {{z}}\left( {l_z}\right)}}}} - {{{2}} {{H}} {{{{l_z}}^{4}}} {{\partial_ {{z}}\left( H\right)}}}}\end{matrix} \right]}}$