question1

[alejandrito20]

ansatz is [math]g_{mn}dy^mdy^n+W^2(y)g_{uv}(x)dx^udx^v[/math]

 

if [math]R_{uv}=\tilde{R}_{uv}-\frac{g_{uv}}{(p+1)W^{p-1}}\nabla^2W^{p+1}[/math] eq1

 

why eq 1 is???

 

[math]\frac{1}{p+1}(\tilde{R}W^{-2}-R)=pW^{-2}\nabla W \nabla W+W^{-1}\nabla^2W[/math]

 

i tried to multiplicate eq1 by [math]W^{-2}g^{uv}[/math] but i don't go to the result

[Amr Morsi]

It will get to the result, alejandrito. Where is the difficulty? Is it the right hand side?

[alejandrito20]

It will get to the result, alejandrito. Where is the difficulty? Is it the right hand side?

 

to multiplicate by [math]W^{-2} g^{uv}[/math]

 

[math]R-W^{-2}\tilde{R}=-\frac{\nabla^2 (W^{p+1})}{W^{p+1}}[/math]

 

[math]\nabla^2(W^{p+1})=P(P+1)W^{P-1}\nabla W \nabla W+(P+1) W^P \nabla ^2 W[/math]

 

Ok......Sorry

 

I tried very time.......gap in my mind..........i'm crazy.........