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h ij <br />
∂2hij 2 N<br />
−<br />
∂t2 ψ4 ∆hij ∂h<br />
− 2Lβ<br />
ij<br />
∂t + LβLβh ij = L ∂β h<br />
∂t<br />
ij<br />
+ 4<br />
<br />
k ∂<br />
Dkβ − Lβ h<br />
3 ∂t ij − N<br />
ψ6 DkQ D i h jk + D j h ik − D k h ij<br />
+ 1<br />
<br />
∂<br />
∂<br />
− Lβ N − Lβ h<br />
N ∂t ∂t ij − 2<br />
3 Dkβ k h ij + (Lβ) ij<br />
<br />
+ 2<br />
<br />
∂<br />
− Lβ Dkβ<br />
3 ∂t k − 2<br />
3 (Dkβ k ) 2<br />
<br />
h ij + 2NS ij<br />
−<br />
<br />
∂<br />
− Lβ<br />
∂t<br />
<br />
<br />
(Lβ) ij + 2<br />
3 Dkβ k (Lβ) ij , <br />
(Lβ) ij = D i β j + D j β i − 2<br />
3 Dkβ k f ij . <br />
h ij <br />
<br />
<br />
<br />
h ij A ij <br />
A ij = 1<br />
2N<br />
<br />
(Lβ) ij + ∂hij<br />
∂t − Lβh ij − 2<br />
3 Dkβ k h ij<br />
<br />
. <br />
<br />
<br />
<br />
<br />
h ij <br />
∂h ij<br />
∂t <br />
<br />
h ij<br />
<br />
<br />
<br />
<br />
h ij