I have two questions...let's suppose we have a metric in the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] ds^2 =f(t)dt^2 +g(x)dx^2 +H(y)dy^2 [/tex]

So every element of the metric only depend on a variable..my question is..does this mean that the Einstein Equations (vaccuum) are of the form:

[tex] R_ii =0 [/tex] i=t,x,y ?..

-And the second question is i know that [tex] det(g_ab )=f(t)g(x)H(y) [/tex] but ..what's the form of the Lagrangian?..i guess:

[tex] L= \int_ V dVf(t)g(x)H(y)(f(t)R_00 +g(x)R_11+ H(y)R_22 ) [/tex]

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