THÈSE Nicolas VASSET
THÈSE Nicolas VASSET THÈSE Nicolas VASSET
p ∈ M V ∋ p M, gµν ηµν M = R 4 ds 2 = −dt 2 + dr 2 + r 2 (dθ 2 + 2 θdϕ 2 ). M, ηµν ( ˜ M, ηµν) ˜ ˜ηµν = Ω −2 ηµν, Ω R 4 d˜s 2 = −dT 2 + dR 2 + 2 R(dθ 2 + 2 θdϕ 2 ). T R −π < T + R < π, −π < T − R < π, 0 ≤ R. ˜ M
R × S 3 S 3 × R R T θ ϕ M R = 0, T = ±π i − i + i 0 I − I + Ω Ω(i 0 ) = Ω(I − ) = Ω(I + ) = 0 ˜ ∇µΩ = 0 I − I + ˜ ∇µ r = cste t = cste π 4 R 4
- 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 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
p ∈ M <br />
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M, gµν<br />
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ηµν <br />
M = R 4 <br />
ds 2 = −dt 2 + dr 2 + r 2 (dθ 2 + 2 θdϕ 2 ). <br />
M, ηµν<br />
( ˜ M, ηµν) ˜ <br />
˜ηµν = Ω −2 ηµν, <br />
Ω R 4 <br />
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d˜s 2 = −dT 2 + dR 2 + 2 R(dθ 2 + 2 θdϕ 2 ). <br />
T R <br />
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−π < T + R < π, <br />
−π < T − R < π, <br />
0 ≤ R. <br />
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˜ M
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