THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
A h µ h X ˜ B h rr h W h η h τ A ˜ B h µ h X ℓ ≥ 2 r ℓ−2 h rr h η h W A ˜ B (∆θϕ + 2)A = − ∂2 h µ ∂A ∂r + 2A r = ∂2hX ∂t , ∂t2 , . 2 h µ h X
∂ 2 L ℓm 0 ∂ 2 E ℓm 1 ∂t 2 ∂ 2 E ℓm 2 ∂t 2 ∂ 2 (L ℓm 0 + T ℓm 0 ) ∂t 2 ∂t2 1 (ℓ + 1)(ℓ + 2) = − Ĉ (2ℓ + 1)r 2 ℓm − ℓ(ℓ + 1)(ℓ − 1) ˜ B ℓm 1 = (ℓ + 1)(ℓ − 1) (2ℓ + 1)r ˜ B ℓm ℓ + 2 + Ĉ 2 ℓm 1 (ℓ + 1) ∂ = 2ℓ + 1 2 ˜ Bℓm 1 ∂ − ∂r 4 Ĉℓm (ℓ + 1)(ℓ + 2) ˜B − ∂r 2 ℓm ℓ − 3 Ĉ − r 4 ℓm r 1 (ℓ + 1)(ℓ + 2) ∂ = 2ℓ + 1 2 Ĉℓm ∂r − ℓ(ℓ + 1)(ℓ + 2)∂ ˜ Bℓm ∂r + ℓ(ℓ + 1)(ℓ − 1)2 ˜ Bℓm r + 1 Ĉℓm (ℓ + 1) [ℓ(ℓ − 3) + ℓ + 4] . 2 r ∂ 2 E ℓm 2 ∂t 2 = 1 (ℓ + 1) 2ℓ(ℓ + 1)(2ℓ + 1) ∂Ĉℓm ∂r + 2ℓ(ℓ + 1)∂ ˜ Bℓm ∂r − ℓ(ℓ + 1)(ℓ − 3) ˜ Bℓm r (ℓ + 1)(ℓ + 4) Ĉ + 2 ℓm r . ˜ B ˜ B Ĉ ℓ ˜B ℓm r = (ℓ + 1)(ℓ − 1) ∂2Lℓm 0 ∂t2 + (ℓ + 1)∂2 Eℓm 1 ∂t2 , ˜B h µ h X A ˜ B h rr h η h W β ij 0 H
- Page 13 and 14: e
- 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 60 and 61: ∂ 2 A = ∆A, ∂t2 ∂2B C =
- Page 62 and 63: h rr h η h W (ℓ + 2) ∂Eℓm
- 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)
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A <br />
h µ h X <br />
˜ B h rr h W h η<br />
h τ <br />
<br />
A ˜ B<br />
<br />
<br />
<br />
<br />
h µ h X <br />
<br />
<br />
ℓ ≥ 2 <br />
r ℓ−2 <br />
<br />
<br />
h rr h η h W<br />
A ˜ B <br />
<br />
<br />
<br />
(∆θϕ + 2)A = − ∂2 h µ<br />
∂A<br />
∂r<br />
+ 2A<br />
r = ∂2hX ∂t<br />
,<br />
∂t2 <br />
, . 2 <br />
h µ h X
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