THÈSE Nicolas VASSET

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(Σt, γij, Kij) Σt St s i St q i j = γ i j − s i sj. l Θij = N(Dmsn − Kmn)q m iq n j, θ (l) = N(Dis i + Kijs i s j − K). St ˜s i = ψ 2 s i θ (l) = 0 4˜s i ˜ Diψ + ˜ Di˜s i + ψ −2 Kij˜s i ˜s j − ψ 2 K = 0.
ψ ∂ ∂t µ = Nn µ + β µ St s i ˜s i β i = bs i − V i = ˜ b˜s i − V i , St ˜ N b = . ψ2 σ (l) ab St V i ∂ ∂t ˜γij = 0, St qbc (2) DaV c + qac (2) DbV c − qab (2) DcV c = 0, (2) D St V i κ κ = s i DiN − NKijs i s j + L(l)(N), St
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h ij
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
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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 ∆
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(r, θ, ϕ) R 3 (
Page 46 and 47:
f N 0
Page 48 and 49:
H f {fi} H
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R 3
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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 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 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
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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 (
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 (
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ψ 2 α (b−N) = 1000 µ (
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THÈSE Nicolas VASSET

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