THÈSE Nicolas VASSET

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Σ ( ∂ ∂ϕ )µ H Σ S l µ = ( ∂ ∂t )µ + Ω( ∂ ∂ϕ )µ k µ S kµl µ = −1 κ = −∇µlνk ν l µ . δM = κ 8π δA + ΩδJ, A t J Ω
St H l µ k µ St qµν gµν St v µ St Θ (v) µν = ∇αvβq α µq β ν = 1 2 qµ αq ν βLvqµν. qµν v θ (v) σ (l) µν v θ (v) = q µ Θ (v) µν σ (l) µν = Θ (v) µν − 1 2 θ(v) qµν. θ (v) ɛ S µν qµν St Lvɛ S µν = θ (v) ɛ S µν, σ (l) µν l H Ω (l) µ = −kα∇βl α q β µ. q α Ω µLl (l) α 8π + θ(l) Ω(l) µ 8π = Tαβl α q β µ + 1 (2) Dµ 8π κ + θ(l) − 2 1 (2) Dασ 8π (l)α µ, κ (2) Dµ qµν St q α µLlπ (l) α + θ (l) π (l) µ = − (2) DµP + 2µ (2) Dασ (l)α µ + ζ (2) Dµθ (l) + f. Πµ = − 1 8π Ω(l) µ κ 8π = P Tαβlαq β µ = fµ
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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 (
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
Page 90 and 91: ∂ µ ∂t ∂ µ µ
Page 92 and 93: mi Mi N
Page 94 and 95: X i ψ
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
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
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H (1−ɛA) r
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ɛA ɛP A JK λ
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(1 − ɛA) NH = 0.5
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ɛP A NH = 0.55
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Σt St
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(b − N) (b − N) = −Cθ
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t0
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S t = t0
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αN = 1000 µN = 1
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ψ 2 α (b−N) = 1000 µ (
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ψ 2 α (b−N) = 1000 µ (
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ψ 2 α (b−N) = 1000 µ (
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ψ 2 α (b−N) = 1000 µ (
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ψ 2 α (b−N) = 1000 µ (
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ψ 2 α (b−N) = 1000 µ (
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ψ 2 α (b−N) = 1000 µ (
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THÈSE Nicolas VASSET

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