THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
= R > 0 ∀(θ, ϕ) ∀t ≥ 0, h ij (t, R, θ, ϕ) = ζ ij 0 (t, θ, ϕ). A ˜ B h µ h X r = 0 h rr h η h W R 3 h µ h X h rr h η h W ϕ θ P m ℓ (cosθ) ∆θϕ
Nr R = 6, dt = 0, 00032, Nθ = 17, Nϕ = 4 ∂2φ = ∆φ ⇐⇒ ∂t2 ⎧ ⎪⎨ ∂φ = ψ, ∂t ⎪⎩ ∂ψ = ∆φ. ∂t V i 0 (r, θ, ϕ) z = r cos(θ) V x 0 = −V y 0 = cos(z), V i 0 V x (t, r, θ, ϕ) = −V y (t, r, θ, ϕ) = cos(t) cos(z),
- 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 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 64 and 65: A h µ h X ˜
- 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)
- Page 110 and 111: ψ
- Page 112 and 113: ψ
- Page 114 and 115: ˜γij = ψ −4 γij; ψ = 1 (γ
= R > 0 <br />
∀(θ, ϕ) <br />
∀t ≥ 0, h ij (t, R, θ, ϕ) = ζ ij<br />
0 (t, θ, ϕ).<br />
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A ˜ B <br />
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h µ h X <br />
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r = 0 <br />
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h rr h η h W <br />
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R 3 <br />
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h µ<br />
h X h rr h η h W<br />
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ϕ θ <br />
P m ℓ (cosθ) <br />
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∆θϕ
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