THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
Φ = ln(ψ) ∆ S = S µ µ ˜R∗ ˜R∗ = 1 4 ˜γkl Dkh mn Dl˜γmn − 1 2 ˜γkl Dkh mn Dn˜γml. N ∆N = ψ 4 N kl 4π(E + S) + ÃklA − h kl DkDlN − 2 ˜ DkΦ ˜ D k N. β i ∆β i + 1 3 Di Djβ j = 16πNψ 4 J i + 2A ij DjN −12NA ij DjΦ − 2N∆ i klA kl − h kl DkDlβ i − 1 3 hik DkDlβ l . ∆ i kl ∆ k ij = 1 2 ˜γkl (Di˜γlj + Dj˜γil − Dl˜γij) , ˜ D i D i ∂Φ ∂t − βk DkΦ = 1 6 Dkβ k . h ij A ij ∂hij ∂t − Lβh ij − 2 3 Dkβ k h ij = 2NA ij − (Lβ) ij , ∂A ij ∂t − LβA ij − 2 3 Dkβ k A ij = N 2ψ4 ∆hij + S ij − 1 2ψ6 i jk j ik k ij D h + D h − D h DkQ. S ij
h ij ∂2hij 2 N − ∂t2 ψ4 ∆hij ∂h − 2Lβ ij ∂t + LβLβh ij = L ∂β h ∂t ij + 4 k ∂ Dkβ − Lβ h 3 ∂t ij − N ψ6 DkQ D i h jk + D j h ik − D k h ij + 1 ∂ ∂ − Lβ N − Lβ h N ∂t ∂t ij − 2 3 Dkβ k h ij + (Lβ) ij + 2 ∂ − Lβ Dkβ 3 ∂t k − 2 3 (Dkβ k ) 2 h ij + 2NS ij − ∂ − Lβ ∂t (Lβ) ij + 2 3 Dkβ k (Lβ) ij , (Lβ) ij = D i β j + D j β i − 2 3 Dkβ k f ij . h ij h ij A ij A ij = 1 2N (Lβ) ij + ∂hij ∂t − Lβh ij − 2 3 Dkβ k h ij . h ij ∂h ij ∂t h ij h ij
- Page 10 and 11: h ij
- Page 13 and 14: e
- Page 15 and 16: 10 5
- Page 17: (−, +, +, +)
- Page 20 and 21: Rµν − 1 2 gµνR = 8πG c 4 Tµ
- Page 22 and 23: ∇µG µν = ∇µ( (4) R µν −
- Page 24 and 25: p ∈ M V ∋ p
- Page 26 and 27: R × S 3
- Page 28 and 29: n µ Σt Σt
- Page 30 and 31: E Jα Sαβ
- Page 32 and 33: N = 1, β i = 0
- Page 34 and 35: M N β i
- Page 36 and 37: ∂ ∂t fij = 0 ˜γij =
- Page 38 and 39: (γij, Kij) Σt0
- Page 42 and 43: h ij ∂2hij 2 N − ∂t2 ψ4 ∆
- Page 44 and 45: (r, θ, ϕ) R 3 (
- Page 46 and 47: f N 0
- Page 48 and 49: H f {fi} H
- Page 50 and 51: R 3
- Page 52 and 53: V R ∀(θ, ϕ) ∀t
- Page 54 and 55: ∇ · D0 = 0 W W µ
- Page 56 and 57: A V r V η
- Page 58 and 59: h = h rr + h τ . h τ
- Page 60 and 61: ∂ 2 A = ∆A, ∂t2 ∂2B C =
- Page 62 and 63: h rr h η h W (ℓ + 2) ∂Eℓm
- Page 64 and 65: A h µ h X ˜
- Page 66 and 67: = R > 0 ∀(θ, ϕ) ∀t
- Page 68 and 69: dt R = 6, Nr = 17, Nθ = 17,
- Page 70 and 71: dt R = 6, Nr = 17, Nθ = 17,
- Page 72 and 73: A, A, ˜ B
- Page 74 and 75: p (M, ηµν) D + (p)
- Page 76 and 77: ∗ = r + 2M r 2M − 1 .
- Page 78 and 79: T = 0
- Page 80 and 81: (x, y, z, t) r(xdx + ydy) −
- Page 82 and 83: ∂ µ ∂t
- Page 84 and 85: = 2M r = 0
- Page 86 and 87: θ (ξ)
- Page 88 and 89: a 2 > M 2
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
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