THÈSE Nicolas VASSET

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∗ = r + 2M r 2M − 1 . u = t + r ∗ v = t − r ∗ . U = e −u/4M V = e v/4M . T = U + V 2 R = U − V 2 . r 1/2 T = ± − 1 e 2M r/4M t , 4M r 1/2 R = ± − 1 e 2M r/4M t (r ≥ 2M), 4M T = ± 1 − r 1/2 e 2M r/4M t , 4M R = ± 1 − r 1/2 e 2M r/4M t (r ≤ 2M), 4M
(R, T ) (r, t) ds 2 = 32M 3 e r/2M r (−dT 2 + dR 2 ) + r 2 (dθ 2 + 2 θdϕ 2 ). r = 2M (r, t, θ, ϕ) r = 0 R µνρσRµνρσ M 2 r6 (t, r) ↔ (T, R) (t, r) (T, R) (M∗ , g∗ µν) r = 2M M M (R, T )
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h ij
Page 13 and 14:
e
Page 15 and 16:
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
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 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 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 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
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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
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S t = t0
Page 162 and 163:
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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