THÈSE Nicolas VASSET

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A h µ h X ˜ B h rr h W h η h τ A ˜ B h µ h X ℓ ≥ 2 r ℓ−2 h rr h η h W A ˜ B (∆θϕ + 2)A = − ∂2 h µ ∂A ∂r + 2A r = ∂2hX ∂t , ∂t2 , . 2 h µ h X
∂ 2 L ℓm 0 ∂ 2 E ℓm 1 ∂t 2 ∂ 2 E ℓm 2 ∂t 2 ∂ 2 (L ℓm 0 + T ℓm 0 ) ∂t 2 ∂t2 1 (ℓ + 1)(ℓ + 2) = − Ĉ (2ℓ + 1)r 2 ℓm − ℓ(ℓ + 1)(ℓ − 1) ˜ B ℓm 1 = (ℓ + 1)(ℓ − 1) (2ℓ + 1)r ˜ B ℓm ℓ + 2 + Ĉ 2 ℓm 1 (ℓ + 1) ∂ = 2ℓ + 1 2 ˜ Bℓm 1 ∂ − ∂r 4 Ĉℓm (ℓ + 1)(ℓ + 2) ˜B − ∂r 2 ℓm ℓ − 3 Ĉ − r 4 ℓm r 1 (ℓ + 1)(ℓ + 2) ∂ = 2ℓ + 1 2 Ĉℓm ∂r − ℓ(ℓ + 1)(ℓ + 2)∂ ˜ Bℓm ∂r + ℓ(ℓ + 1)(ℓ − 1)2 ˜ Bℓm r + 1 Ĉℓm (ℓ + 1) [ℓ(ℓ − 3) + ℓ + 4] . 2 r ∂ 2 E ℓm 2 ∂t 2 = 1 (ℓ + 1) 2ℓ(ℓ + 1)(2ℓ + 1) ∂Ĉℓm ∂r + 2ℓ(ℓ + 1)∂ ˜ Bℓm ∂r − ℓ(ℓ + 1)(ℓ − 3) ˜ Bℓm r (ℓ + 1)(ℓ + 4) Ĉ + 2 ℓm r . ˜ B ˜ B Ĉ ℓ ˜B ℓm r = (ℓ + 1)(ℓ − 1) ∂2Lℓm 0 ∂t2 + (ℓ + 1)∂2 Eℓm 1 ∂t2 , ˜B h µ h X A ˜ B h rr h η h W β ij 0 H
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h ij
Page 13 and 14: e
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 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 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
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h ij h ij D
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h ij
Page 120 and 121:
A ∆A − ψ4 N 2 LβLβA = A
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∆h µ + 2 ∂h r µ ∂r ∆h η
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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
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˜γ ij
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h ij A ˜ B
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H IJ A ˜ B
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AHE = 8π(M 2 ADM + M 4 ADM − J
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MHawking(S2) ≥ MHawking(S1) S2
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ɛ P := A 16πM 2 ADM ɛ A := ≤ 1
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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
Page 156 and 157:
(b − N) (b − N) = −Cθ
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t0
Page 160 and 161:
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 (
Page 176:
ψ 2 α (b−N) = 1000 µ (
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THÈSE Nicolas VASSET

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