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Dear friends,

Just a small question I do not know how to derive.

From the Einstein-scalar field action defined by

[tex]S\left( {g,\psi } \right) = \int_{} {\left( {R(g) - \frac{1}{2}\left| {\nabla \psi } \right|_g^2 - V\left( \psi \right)} \right)d{\eta _g}}[/tex]

one gets the so-called Einstein-scalar field equations given by

[tex]{\rm Eins}_{\alpha \beta} = {\nabla _\alpha }\psi {\nabla _\beta }\psi - \frac{1}{2}{g_{\alpha \beta }}{\nabla _\mu }\psi {\nabla ^\mu }\psi - {g_{\alpha \beta }}V(\psi ).[/tex]

My question is how to derive such equations. It seems that we need to take derivative.... but how? Thanks.

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# Einstein-scalar field action -> Einstein-scalar field equations

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