THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
f N 0 f N ˜ fi ci f R 3 (r, θ, ϕ) ∀ℓ ≥ 0, ∀m, 0 ≤ m ≤ ℓ, Y m ℓ (θ, ϕ) = e imϕ P m ℓ (cos θ), ∀m, −ℓ ≤ m < 0, Y m ℓ (θ, ϕ) = (−1) m e imϕ P |m| ℓ (cos θ). P m ℓ (ℓ, m) f f(r, θ, ϕ) = ∞ ℓ ℓ=0 m=−ℓ fℓm(r)Y m ℓ (θ, ϕ). fℓm r f Y m ℓ (θ, ϕ)
= 0 f(r, θ, ϕ) = ∞ ℓ ℓ=0 m=−ℓ r ℓ ∞ i=0 fiℓmr 2i Y m ℓ (θ, ϕ). fℓm(r) fℓm(r) ℓ ℓ f(r, θ, ϕ) = ∞ ℓ ∞ ℓ=0 m=−ℓ i=0 fiℓmTi(r)Y m ℓ (θ, ϕ), i ℓ r ℓ Hf(r) = s(r). H { ˜si}i∈[0,N−1] N s { ˜ fi}i∈[0,N−1] N xi Hf(xi) = s(xi) f s N H N H H f {si}
- 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 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 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) −
- 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
f N<br />
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f <br />
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N <br />
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˜ fi <br />
ci <br />
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f R 3<br />
(r, θ, ϕ) <br />
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∀ℓ ≥ 0, ∀m, 0 ≤ m ≤ ℓ, Y m<br />
ℓ (θ, ϕ) = e imϕ P m ℓ (cos θ), <br />
∀m, −ℓ ≤ m < 0, Y m<br />
ℓ (θ, ϕ) = (−1) m e imϕ P |m|<br />
ℓ (cos θ). <br />
P m ℓ (ℓ, m)<br />
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f <br />
f(r, θ, ϕ) =<br />
∞<br />
ℓ<br />
ℓ=0 m=−ℓ<br />
fℓm(r)Y m<br />
ℓ (θ, ϕ). <br />
fℓm r <br />
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f <br />
Y m<br />
ℓ<br />
(θ, ϕ)
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