- #1
bookworm_vn
- 9
- 0
Einstein-scalar field action --> Einstein-scalar field equations
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.
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.