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St H l µ k µ <br />
St <br />
qµν gµν <br />
St v µ St <br />
<br />
Θ (v)<br />
µν = ∇αvβq α µq β ν = 1<br />
2 qµ αq ν βLvqµν. <br />
qµν <br />
v <br />
θ (v) σ (l)<br />
µν <br />
v <br />
θ (v) = q µ Θ (v)<br />
µν σ (l)<br />
µν = Θ (v)<br />
µν − 1<br />
2 θ(v) qµν. <br />
θ (v) ɛ S µν qµν St <br />
Lvɛ S µν = θ (v) ɛ S µν, <br />
σ (l)<br />
µν <br />
<br />
<br />
l H <br />
Ω (l) µ = −kα∇βl α q β µ. <br />
<br />
<br />
q α Ω<br />
µLl<br />
(l) α<br />
8π + θ(l) Ω(l) µ<br />
8π = Tαβl α q β µ + 1 (2)<br />
Dµ<br />
8π<br />
<br />
κ + θ(l)<br />
<br />
−<br />
2<br />
1 (2)<br />
Dασ<br />
8π<br />
(l)α µ, <br />
κ <br />
(2) Dµ qµν St <br />
<br />
<br />
<br />
q α µLlπ (l)<br />
α + θ (l) π (l)<br />
µ = − (2) DµP + 2µ (2) Dασ (l)α µ + ζ (2) Dµθ (l) + f. <br />
<br />
Πµ = − 1<br />
8π Ω(l) µ<br />
κ<br />
8π<br />
<br />
= P <br />
Tαβlαq β µ = fµ