THÈSE Nicolas VASSET

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t0 t = t0 t ≤ t0 t ≥ t0 V i t ≥ t0
t = t0 F S r = rS 1 ∂F N ∂t = µ(∆θϕF − ∆θϕF∞) − α(F − F∞). µ α F∞ F S N = N0 ∈ R + ∞ ℓ F0 = F0ℓmY m ℓ (θ, ϕ). t = t0 ℓ=0 m=−ℓ ∀(t ≥ t0), ∀(ℓ, m), Fℓm(t) = F∞ℓm + (F0ℓm − F∞ℓm)e −N(α+µℓ(ℓ+1))(t−t0) . α µ
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h ij
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e
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10 5
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(−, +, +, +)
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Rµν − 1 2 gµνR = 8πG c 4 Tµ
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∇µG µν = ∇µ( (4) R µν −
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p ∈ M V ∋ p
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R × S 3
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n µ Σt Σt
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E Jα Sαβ
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N = 1, β i = 0
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M N β i
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∂ ∂t fij = 0 ˜γij =
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(γij, Kij) Σt0
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Φ = ln(ψ) ∆ S
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h ij ∂2hij 2 N − ∂t2 ψ4 ∆
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(r, θ, ϕ) R 3 (
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f N 0
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H f {fi} H
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R 3
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V R ∀(θ, ϕ) ∀t
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∇ · D0 = 0 W W µ
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A V r V η
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h = h rr + h τ . h τ
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∂ 2 A = ∆A, ∂t2 ∂2B C =
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h rr h η h W (ℓ + 2) ∂Eℓm
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A h µ h X ˜
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= R > 0 ∀(θ, ϕ) ∀t
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dt R = 6, Nr = 17, Nθ = 17,
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dt R = 6, Nr = 17, Nθ = 17,
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A, A, ˜ B
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p (M, ηµν) D + (p)
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∗ = r + 2M r 2M − 1 .
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T = 0
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(x, y, z, t) r(xdx + ydy) −
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∂ µ ∂t
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= 2M r = 0
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θ (ξ)
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a 2 > M 2
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∂ µ ∂t ∂ µ µ
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mi Mi N
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X i ψ
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Σ (
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θ (l) µ = 1 16π ζ
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(M, gµν) S 2 × R l µ
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2π µ ∂
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St θ (l) = 0 θ (k) < 0.
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¯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
Page 116 and 117: h ij h ij D
Page 118 and 119: h ij
Page 120 and 121: A ∆A − ψ4 N 2 LβLβA = A
Page 122 and 123: ∆h µ + 2 ∂h r µ ∂r ∆h η
Page 124 and 125: h ij h ij
Page 126 and 127: MHΩ JK a M
Page 128 and 129: MH JH MADM
Page 130 and 131: 1 − ɛA M2 M 3
Page 132 and 133: ˜γ ij
Page 134 and 135: h ij A ˜ B
Page 136 and 137: H IJ A ˜ B
Page 138 and 139: AHE = 8π(M 2 ADM + M 4 ADM − J
Page 140 and 141: MHawking(S2) ≥ MHawking(S1) S2
Page 142 and 143: ɛ P := A 16πM 2 ADM ɛ A := ≤ 1
Page 144 and 145: R = r + M 2 − a2 + M, 4r R
Page 146 and 147: H (1−ɛA) r
Page 148 and 149: ɛA ɛP A JK λ
Page 150 and 151: (1 − ɛA) NH = 0.5
Page 152 and 153: ɛP A NH = 0.55
Page 154 and 155: Σt St
Page 156 and 157: (b − N) (b − N) = −Cθ
Page 160 and 161: S t = t0
Page 162 and 163: αN = 1000 µN = 1
Page 164 and 165: ψ 2 α (b−N) = 1000 µ (
Page 166 and 167: ψ 2 α (b−N) = 1000 µ (
Page 168 and 169: ψ 2 α (b−N) = 1000 µ (
Page 170 and 171: ψ 2 α (b−N) = 1000 µ (
Page 172 and 173: ψ 2 α (b−N) = 1000 µ (
Page 174 and 175: ψ 2 α (b−N) = 1000 µ (
Page 176: ψ 2 α (b−N) = 1000 µ (
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THÈSE Nicolas VASSET

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