THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
N = 1, β i = 0 (γij, Kij) Σt (M, gµν) (Σt) (γij, Kij)t fij Σt (x 1 , x 2 , x 3 ) r (γij, Kij) γij = fij + O(r −1 ), ∂γij ∂x k = O(r−2 ), Kij = O(r −2 ), ∂Kij ∂x k = O(r−3 ).
D fij St,r ∈ Σt r r si qab Σt MADM = 1 16π St,r→∞ D j γij − Di(f kl γkl) s i√ qd 2 y. √ qd 2 y St,r q qab d 2 y Σt (M, gµν) k µ MK = − 1 8π St,r ∇ µ k µ (sµnν − nµsν) √ qd 2 y, n µ Σt St (M, gµν) φ i JK = 1 16π St,r ∇ µ φ µ (sµnν − nµsν) √ qd 2 y = 1 8π St,r Kijs i φ i√ qd 2 y.
- Page 10 and 11: 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 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 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) −
N = 1, β i = 0 <br />
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(γij, Kij) Σt <br />
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(M, gµν) <br />
(Σt) (γij, Kij)t <br />
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fij <br />
Σt <br />
(x 1 , x 2 , x 3 ) r<br />
(γij, Kij) <br />
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γij = fij + O(r −1 ),<br />
∂γij<br />
∂x k = O(r−2 ),<br />
Kij = O(r −2 ),<br />
∂Kij<br />
∂x k = O(r−3 ).
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