(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi,

I am given the following action S:

S=1/2∫〖g^ab ((∇_a Ф ∇_b Ф)+(1/6 R_ab Ф^2) ) √(-g) dx^4 〗

Where R_ab is the Ricci tensor, Ф is a scalar field and g^ab is the metric.

I am asked to find the equation of motion for the field.

2. Relevant equations

I know I have to substitute my Lagrangian: L= 1/2 g^ab ((∇_a Ф ∇_b Ф)+(1/6 R_ab Ф^2) )

into the Euler-Lagrange equations, but I don't know in which EL equation exactly!

3. The attempt at a solution

I mean should I use the EL equation where Ф and ∇_b Ф are my independent components? Or should I use the 2nd order EL equations where g_ab; g_ab,c & g_ab,cd are my independent components (as in the Einstein Hilbert action)?

Thanks :)

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: General Relativity-Variational approach

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