THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
∇ · D0 = 0 W W µ W θ ϕ ∂rW η W η W r + − r r W D0 A = ∂W η ∂r + W η r r W − . r D0 = 0 ⇐⇒ W µ = 0 A = 0. V µ A V r V η (∆V) η = ∆V η r V + 2 , r2 (∆V) µ = ∆V µ . µ ∂ 2 V µ ∂t 2 = ∆V µ . A ∂2A = ∆A. ∂t2 V F Φ Ψ F = ∇ × (Ψk) + ∇ × ∇ × (Φk) k eρ
k = er F = − 1 r2 ∆θϕΦer + 1 r 1 sin θ ∂ϕΨ + ∂θ∂rΦ eθ + 1 r −∂θΨ + 1 sin θ ∂ϕ∂rΦ F η F µ F η = 1 r ∂rΦ F µ = − 1 r Ψ A Φ A = 1 r ∂2 r Φ + 1 ∆Φ = ∆ r3 Φ r eϕ. . ∆θϕA = −∆(rF r ). V µ A v0 w0 V µ (t = 0) ∂V µ ∂t A t=0 µ v0 w0 b0 V µ A R [0, T ] V (V r , V η ) V A V r V η A A(t, r, θ, ϕ) = ℓ,m A ℓm (t, r)Y m ℓ (θ, ϕ). ∀ℓ > 0, ∀m − ℓ ≤ m ≤ ℓ, ⎧ ⎪⎨ ⎪⎩ ∂R ℓm ∂r + 2Rℓm r ∂E ℓm ∂r ℓ(ℓ + 1) − E r ℓm = 0 Eℓm Rℓm + − = Aℓm r r .
- 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 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 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
- 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 ∂
k = er <br />
<br />
F = − 1<br />
r2 ∆θϕΦer + 1<br />
r<br />
1<br />
sin θ ∂ϕΨ + ∂θ∂rΦ<br />
<br />
eθ + 1<br />
r<br />
<br />
−∂θΨ + 1<br />
sin θ ∂ϕ∂rΦ<br />
F η F µ <br />
F η = 1<br />
r ∂rΦ<br />
F µ = − 1<br />
r Ψ<br />
A Φ <br />
A = 1<br />
r ∂2 r Φ + 1<br />
∆Φ = ∆<br />
r3 <br />
Φ<br />
r<br />
<br />
eϕ. <br />
<br />
. <br />
∆θϕA = −∆(rF r ). <br />
<br />
<br />
<br />
<br />
<br />
<br />
V µ A v0 w0<br />
V µ (t = 0) ∂V µ<br />
∂t<br />
<br />
A <br />
t=0 µ v0 w0<br />
b0 <br />
V µ A <br />
R [0, T ] <br />
V<br />
(V r , V η ) V <br />
A <br />
<br />
V r V η <br />
A <br />
A(t, r, θ, ϕ) = <br />
ℓ,m<br />
A ℓm (t, r)Y m<br />
ℓ (θ, ϕ). <br />
<br />
∀ℓ > 0, ∀m − ℓ ≤ m ≤ ℓ,<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
∂R ℓm<br />
∂r<br />
+ 2Rℓm<br />
r<br />
∂E ℓm<br />
∂r<br />
ℓ(ℓ + 1)<br />
− E<br />
r<br />
ℓm = 0<br />
Eℓm Rℓm<br />
+ − = Aℓm<br />
r<br />
r<br />
.
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