THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
∂ 2 A = ∆A, ∂t2 ∂2B C = ∆B − , 2 2 ∂t 2r ∂2C 2C = ∆C + ∂t2 r r2 . B C A B C A(t, r, θ, ϕ) = ℓ,m B(t, r, θ, ϕ) = ℓ,m C(t, r, θ, ϕ) = ℓ,m 2 + 8∆θϕB A ℓm (t, r)Y m ℓ (θ, ϕ), B ℓm (t, r)Y m ℓ (θ, ϕ), C ℓm (t, r)Y m ℓ (θ, ϕ). ˜ B Ĉ ˜B(t, r, θ, ϕ) = 2B ℓ,m ℓm (t, r) + Cℓm (t, r) Y 2(ℓ + 1) m ℓ (θ, ϕ), Ĉ(t, r, θ, ϕ) = ℓm ℓm m C (t, r) − 4ℓB (t, r) Yℓ (θ, ϕ). ℓ,m ∂2B˜ ∂t2 = ˜ ∆ ˜ B, ∂2Ĉ ∂t2 = ˆ ∆Ĉ; f(r, θ, ϕ) = (ℓ,m) f ℓm (r)Y m ℓ (θ, ϕ) ˜∆f = ∂2f 2 ∂f + ∂r2 r ∂r ˆ∆f = ∂2f 2 ∂f + ∂r2 r ∂r 1 + r2 + 1 r 2 ℓm ℓm −ℓ(ℓ − 1)f ℓm Y m ℓ −(ℓ + 1)(ℓ + 2)f ℓm Y m ℓ , . 1 ℓ ∆θϕ ˜ ∆ ˆ ∆
h ij ˜γ ij = f ij + h ij 1 h h B C C B ∂C ∂r + 2C r + 2∆θϕ ∂B ∂r + 3B r C − = ∆h. 4r h B r C 0 ˜ B Ĉ h A ˜ B h = 0 A(t, r, θ, ϕ) ˜ B(t, r, θ, ϕ) h t A ˜ B A H µ = 0 h µ h X h ∂B ℓm 2 ∂r ∂B ℓm 1 ∂r Bℓm 1 − r = Aℓm , 3Bℓm 1 + r 2 − ℓ(ℓ + 1)Bℓm 2 + r = 0. ˜ B Hr = Hη = 0
- Page 10 and 11: h ij
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- Page 15 and 16: 10 5
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- 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 40 and 41: Φ = ln(ψ) ∆ S
- 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 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
- Page 90 and 91: ∂ µ ∂t ∂ µ µ
- Page 92 and 93: mi Mi N
- Page 94 and 95: X i ψ
- Page 96 and 97: Σ (
- Page 98 and 99: θ (l) µ = 1 16π ζ
- Page 100 and 101: (M, gµν) S 2 × R l µ
- Page 102 and 103: 2π µ ∂
- Page 104 and 105: St θ (l) = 0 θ (k) < 0.
- Page 106 and 107: ¯κ
- Page 108 and 109: (Σt, γij, Kij)
h ij <br />
˜γ ij = f ij + h ij 1<br />
<br />
<br />
h <br />
h <br />
<br />
B C <br />
C B <br />
<br />
∂C<br />
∂r<br />
+ 2C<br />
r<br />
+ 2∆θϕ<br />
∂B<br />
∂r<br />
+ 3B<br />
r<br />
<br />
C<br />
− = ∆h.<br />
4r<br />
h B <br />
r C 0 <br />
˜ B Ĉ <br />
<br />
h <br />
<br />
<br />
A ˜ B <br />
<br />
<br />
<br />
<br />
h = 0 <br />
<br />
<br />
A(t, r, θ, ϕ) ˜ B(t, r, θ, ϕ) <br />
h t <br />
<br />
<br />
A ˜ B <br />
<br />
<br />
A H µ = 0 <br />
h µ h X h <br />
∂B ℓm<br />
2<br />
∂r<br />
∂B ℓm<br />
1<br />
∂r<br />
Bℓm 1<br />
−<br />
r = Aℓm , <br />
3Bℓm 1<br />
+<br />
r<br />
2 − ℓ(ℓ + 1)Bℓm 2<br />
+<br />
r<br />
= 0. <br />
˜ B <br />
Hr = Hη = 0
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