THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
∗ = 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 )
- 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
(R, T ) <br />
(r, t) <br />
<br />
<br />
<br />
ds 2 = 32M 3 e r/2M<br />
r<br />
(−dT 2 + dR 2 ) + r 2 (dθ 2 + 2 θdϕ 2 ). <br />
<br />
r = 2M <br />
(r, t, θ, ϕ) r = 0 <br />
R µνρσRµνρσ <br />
M 2<br />
r6 <br />
<br />
<br />
<br />
(t, r) ↔ (T, R) <br />
(t, r) <br />
(T, R) <br />
(M∗ , g∗ µν) <br />
r = 2M <br />
M <br />
<br />
M <br />
(R, T )
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