THÈSE Nicolas VASSET

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A ∆A − ψ4 N 2 LβLβA = AS(h ij , N, ψ, β, Âij ). A A ψ 4 N 2 LβLβA = ψ4 N 2 (βr ) 2 ∂ 2 r A + ψ4 N 2 (LβLβA) ∗ ; A = AlmYlm(θ, ϕ), (l,m) Ylm (l, m) ∆θϕYlm = −l(l + 1)Ylm β r = ˜ b √˜γ rr = N Ψ2√ . ˜γ rr l = 0 (β r )(l=0) = ( N ψ2 )(l=0) l = 0 rH ψ 4 N 2 (βr ) 2 ∂ (l=0) 2 r A = [1 + α(r − rH) + δ(r − rH) 2 + O(r − rH) 3 ]∂ 2 r A, α δ N ψ β r
A l −α(r − rH) − δ(r − rH) 2 ∂ 2 − l(l + 1) r 2 ∂r 2 Alm + 2 r ∂ ∂r Alm Alm = AS + ψ4 ∗∗ (LβLβA) N 2 lm, ∗∗ ψ4 N 2 (β r ) 2 Qαδ α δ Qαδ = −α(r − rH) − δ(r − rH) 2 ∂ 2 + 2 r ∂ ∂r ∂r 2 − l(l + 1) r 2 I, R 3 Qαδ Qαδf = Sf 4 ˜Q ψ = N 2 (βr ) 2 (l=0) ∂2 2 + ∂r2 r ∂ ∂r − l(l + 1) r 2 I ˜ B ˜ ∆ ˜ B h ij h rr h η h µ h ij
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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,
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
Page 116 and 117: h ij h ij D
Page 118 and 119: h ij
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 158 and 159: t0
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 (
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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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