THÈSE Nicolas VASSET

∇ Y E ℓm Y B ℓm
Y R ℓm
V
V η (t, r, θ, ϕ) =
ℓ,m
V µ (t, r, θ, ϕ) =
ℓ,m
ℓ,m
E ℓm Y m
ℓ ,
B ℓm Y m
ℓ ,
R ℓm Y m
ℓ = V r .
(V η , V µ )
∆θϕV η =
∆θϕV µ =
V θ η ∂V 1
= −
∂θ sin θ
V ϕ = 1 ∂V
sin θ
η µ ∂V
+
∂ϕ ∂θ ;
θ ∂V
∂θ
ϕ ∂V
∂θ
θ V 1
+ +
tan θ sin θ
∂V µ
,
∂ϕ
∂V ϕ
∂ϕ
ϕ V 1
+ −
tan θ sin θ
,
∂V θ
.
∂ϕ
θ ∈ [0, π], ϕ ∈ [0, 2π[
V θ , V ϕ
(V η , V µ ) V η V µ
ℓ = 0
(V r , V η , V µ )
W
Θ =
∂W r
∂r
+ 2W r
r
+ 1
r ∆θϕW η ;
W η
R 3
W = ∇φ + D0,