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Display information for equation id:math.1109.280 on revision:1109

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TeX (original user input):

\begin{align}
  & R=\frac{1}{\sqrt{-g}}{{\left[ \sqrt{-g}\left( -{{g}^{\mu }}^{\nu }\Gamma _{\mu \nu }^{\alpha }+{{g}^{\mu }}^{\alpha }\Gamma _{\mu \nu }^{\nu } \right) \right]}_{,\alpha }}+{{L}_{E}}\left( g,\Gamma  \right) \\ 
 & {{L}_{E}}={{g}^{\mu }}^{\nu }\left( \Gamma _{\mu \nu }^{\alpha }\Gamma _{\alpha \beta }^{\beta }-\Gamma _{\mu \beta }^{\alpha }\Gamma _{\nu \alpha }^{\beta } \right) \\ 
 & {{S}_{EH}}=\int\limits_{{{V}_{4}}}{\left( {{L}_{E}}+2\kappa {{L}_{Mat}} \right)\sqrt{-g}{{d}^{4}}x}+\int\limits_{{{V}_{4}}}{\frac{1}{\sqrt{-g}}{{\left[ \sqrt{-g}\left( -{{g}^{\mu }}^{\nu }\Gamma _{\mu \nu }^{\alpha }+{{g}^{\mu }}^{\alpha }\Gamma _{\mu \nu }^{\nu } \right) \right]}_{,\alpha }}\sqrt{-g}{{d}^{4}}x} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&R={\frac {1}{\sqrt {-g}}}{{\left[{\sqrt {-g}}\left(-{{g}^{\mu }}^{\nu }\Gamma _{\mu \nu }^{\alpha }+{{g}^{\mu }}^{\alpha }\Gamma _{\mu \nu }^{\nu }\right)\right]}_{,\alpha }}+{{L}_{E}}\left(g,\Gamma \right)\\&{{L}_{E}}={{g}^{\mu }}^{\nu }\left(\Gamma _{\mu \nu }^{\alpha }\Gamma _{\alpha \beta }^{\beta }-\Gamma _{\mu \beta }^{\alpha }\Gamma _{\nu \alpha }^{\beta }\right)\\&{{S}_{EH}}=\int \limits _{{V}_{4}}{\left({{L}_{E}}+2\kappa {{L}_{Mat}}\right){\sqrt {-g}}{{d}^{4}}x}+\int \limits _{{V}_{4}}{{\frac {1}{\sqrt {-g}}}{{\left[{\sqrt {-g}}\left(-{{g}^{\mu }}^{\nu }\Gamma _{\mu \nu }^{\alpha }+{{g}^{\mu }}^{\alpha }\Gamma _{\mu \nu }^{\nu }\right)\right]}_{,\alpha }}{\sqrt {-g}}{{d}^{4}}x}\\\end{aligned}}

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\begin{aligned} R = \frac{1}{\sqrt{- g}} {[\sqrt{- g} (- {g^{μ}}^{ν} Γ_{μ ν}^{α} + {g^{μ}}^{α} Γ_{μ ν}^{ν})]}_{, α} + L_{E} (g, Γ) \\ L_{E} = {g^{μ}}^{ν} (Γ_{μ ν}^{α} Γ_{α β}^{β} - Γ_{μ β}^{α} Γ_{ν α}^{β}) \\ S_{E H} = \int_{V_{4}} (L_{E} + 2 κ L_{M a t}) \sqrt{- g} d^{4} x + \int_{V_{4}} \frac{1}{\sqrt{- g}} {[\sqrt{- g} (- {g^{μ}}^{ν} Γ_{μ ν}^{α} + {g^{μ}}^{α} Γ_{μ ν}^{ν})]}_{, α} \sqrt{- g} d^{4} x \end{aligned}

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Translations to Computer Algebra Systems

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Identifiers

$R$

$g$

$g$

$g$

$μ$

$ν$

$Γ$

$μ$

$ν$

$α$

$g$

$μ$

$α$

$Γ$

$μ$

$ν$

$ν$

$α$

$L_{E}$

$g$

$Γ$

$L_{E}$

$g$

$μ$

$ν$

$Γ$

$μ$

$ν$

$α$

$Γ$

$α$

$β$

$β$

$Γ$

$μ$

$β$

$α$

$Γ$

$ν$

$α$

$β$

$S_{E H}$

$V_{4}$

$L_{E}$

$κ$

$L_{M a t}$

$g$

$x$

$V_{4}$

$g$

$g$

$g$

$μ$

$ν$

$Γ$

$μ$

$ν$

$α$

$g$

$μ$

$α$

$Γ$

$μ$

$ν$

$ν$

$α$

$g$

$x$

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