${{{ g} _a} _b} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} -{a} & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & c & 0 \\ 0 & 0 & 0 & c\end{matrix} \right]}}$ ${{{ g} ^a} ^b} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} -{\frac{1}{a}} & 0 & 0 & 0 \\ 0 & \frac{1}{b} & 0 & 0 \\ 0 & 0 & \frac{1}{c} & 0 \\ 0 & 0 & 0 & \frac{1}{c}\end{matrix} \right]}}$
conn from manual metric: ${{{{ \Gamma} ^a} _b} _c} = {\overset{a\downarrow[{b\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & \frac{\partial_ {{x}}\left( a\right)}{{{2}} {{a}}} & 0 & 0 \\ \frac{\partial_ {{x}}\left( a\right)}{{{2}} {{a}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix} \right]} \\ \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} \frac{\partial_ {{x}}\left( a\right)}{{{2}} {{b}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & -{\frac{\partial_ {{x}}\left( c\right)}{{{2}} {{b}}}} & 0 \\ 0 & 0 & 0 & -{\frac{\partial_ {{x}}\left( c\right)}{{{2}} {{b}}}}\end{matrix} \right]} \\ \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & \frac{\partial_ {{x}}\left( c\right)}{{{2}} {{c}}} & 0 \\ 0 & \frac{\partial_ {{x}}\left( c\right)}{{{2}} {{c}}} & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix} \right]} \\ \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{\partial_ {{x}}\left( c\right)}{{{2}} {{c}}} \\ 0 & 0 & 0 & 0 \\ 0 & \frac{\partial_ {{x}}\left( c\right)}{{{2}} {{c}}} & 0 & 0\end{matrix} \right]}\end{matrix} \right]}}$ vs manual conn: ${{{{ \Gamma} ^a} _b} _c} = {\overset{a\downarrow[{b\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & E & 0 & 0 \\ E & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix} \right]} \\ \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} -{E} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & E & 0 \\ 0 & 0 & 0 & E\end{matrix} \right]} \\ \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix} \right]} \\ \overset{b\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}}$
Ricci from manual metric
${{{ R} _a} _b} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} \frac{{{{{2}} {{a}} {{c}} {{\partial_{{{x}}{{x}}}\left( a\right)}}} - {{{c}} {{{\partial_ {{x}}\left( a\right)}^{2}}}}} + {{{2}} {{a}} {{\partial_ {{x}}\left( a\right)}} {{\partial_ {{x}}\left( c\right)}}}}{{{4}} {{a}} {{b}} {{c}}} & 0 & 0 & 0 \\ 0 & \frac{{{{{{c}^{2}}} {{{\partial_ {{x}}\left( a\right)}^{2}}}} - {{{2}} {{a}} {{{c}^{2}}} {{\partial_{{{x}}{{x}}}\left( a\right)}}}} + {{{{2}} {{{a}^{2}}} {{{\partial_ {{x}}\left( c\right)}^{2}}}} - {{{4}} {{c}} {{{a}^{2}}} {{\partial_{{{x}}{{x}}}\left( c\right)}}}}}{{{4}} {{{a}^{2}}} {{{c}^{2}}}} & 0 & 0 \\ 0 & 0 & -{\frac{{{{\partial_ {{x}}\left( c\right)}} {{\partial_ {{x}}\left( a\right)}}} + {{{2}} {{a}} {{\partial_{{{x}}{{x}}}\left( c\right)}}}}{{{4}} {{a}} {{b}}}} & 0 \\ 0 & 0 & 0 & -{\frac{{{{\partial_ {{x}}\left( c\right)}} {{\partial_ {{x}}\left( a\right)}}} + {{{2}} {{a}} {{\partial_{{{x}}{{x}}}\left( c\right)}}}}{{{4}} {{a}} {{b}}}}\end{matrix} \right]}}$
vs Ricci from manual conn
${{{ R} _a} _b} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {E}^{2} & 0 & 0 & 0 \\ 0 & -{{E}^{2}} & 0 & 0 \\ 0 & 0 & {E}^{2} & 0 \\ 0 & 0 & 0 & {E}^{2}\end{matrix} \right]}}$
vs desired Ricci
${{{ R} _a} _b} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {E}^{2} & 0 & 0 & 0 \\ 0 & -{{E}^{2}} & 0 & 0 \\ 0 & 0 & {E}^{2} & 0 \\ 0 & 0 & 0 & {E}^{2}\end{matrix} \right]}}$
manual metric Gaussian -- equal to zero according to EM stress-energy trace:
${{G} = {\frac{{{{{a}^{2}}} {{{\partial_ {{x}}\left( c\right)}^{2}}}} + {{{{{{{c}^{2}}} {{{\partial_ {{x}}\left( a\right)}^{2}}}} - {{{2}} {{a}} {{{c}^{2}}} {{\partial_{{{x}}{{x}}}\left( a\right)}}}} - {{{2}} {{a}} {{c}} {{\partial_ {{x}}\left( a\right)}} {{\partial_ {{x}}\left( c\right)}}}} - {{{4}} {{c}} {{{a}^{2}}} {{\partial_{{{x}}{{x}}}\left( c\right)}}}}}{{{2}} {{b}} {{{a}^{2}}} {{{c}^{2}}}}}} = {0}$
${{{{{a}^{2}}} {{{\partial_ {{x}}\left( c\right)}^{2}}}} + {{{{{{{c}^{2}}} {{{\partial_ {{x}}\left( a\right)}^{2}}}} - {{{2}} {{a}} {{{c}^{2}}} {{\partial_{{{x}}{{x}}}\left( a\right)}}}} - {{{2}} {{a}} {{c}} {{\partial_ {{x}}\left( a\right)}} {{\partial_ {{x}}\left( c\right)}}}} - {{{4}} {{c}} {{{a}^{2}}} {{\partial_{{{x}}{{x}}}\left( c\right)}}}}} = {0}$

${{{{{ R} ^a} _b} _c} _d} = {{{{{{{{{ \Gamma} ^a} _b} _d} _{,c}} - {{{{{ \Gamma} ^a} _b} _c} _{,d}}} + {{{{{{ \Gamma} ^a} _e} _c}} {{{{{ \Gamma} ^e} _b} _d}}}} - {{{{{{ \Gamma} ^a} _e} _d}} {{{{{ \Gamma} ^e} _b} _c}}}} - {{{{{{ \Gamma} ^a} _b} _e}} {{\left({{{{{ \Gamma} ^e} _d} _c} - {{{{ \Gamma} ^e} _c} _d}}\right)}}}}$
${{{ R} _a} _b} = {{{{{{{{{ \Gamma} ^c} _a} _b} _{,c}} - {{{{{ \Gamma} ^c} _a} _c} _{,b}}} + {{{{{{ \Gamma} ^c} _d} _c}} {{{{{ \Gamma} ^d} _a} _b}}}} - {{{{{{ \Gamma} ^c} _d} _b}} {{{{{ \Gamma} ^d} _a} _c}}}} - {{{{{{ \Gamma} ^c} _a} _d}} {{\left({{{{{ \Gamma} ^d} _b} _c} - {{{{ \Gamma} ^d} _c} _b}}\right)}}}}$
Gravitation acting on an object at rest is given as ${\Gamma^j}_{tt}$. For a uniform field in the x direction, for the connections that give rise to this stress-energy, gravitation is ${\Gamma^x}_{tt} = -E$.
Applying ${{\frac{3}{2}}} {{V}}$ between conductors ${{0.01}} {{m}}$ apart produces a uniform electric field of ${E} = {{{7.677747990993\cdot{10^{17}}}} \cdot {{\frac{1}{5.118498660662\cdot{10^{15}}}}} {{V}} {{\frac{1}{m}}}}$ .
converting to meters gives ${{E} = {¿}} = {¿}$