Magnetized Accretion onto Inspiraling Binary Black Holes - LUTH

Error Analysis: Ricci Tensor and Ricci Scalar
Christoffel symbols and derivatives:
Γ ρ µν = 1
2 g ρσ [gνσ,µ + gµσ,ν − gµν,σ]
Ricci Tensor:
Γ ρ
µν,λ
= 1
2 g ρσ ,λ [gνσ,µ + gµσ,ν − gµν,σ]
+ 1
2 g ρσ [gνσ,µλ + gµσ,νλ − gµν,σλ]
Rµρ = Γ ν µρ,ν − Γ ν νρ,µ + Γ α µρΓ ν αν − Γ α νρΓ ν αµ
Ricci Scalar: R = R µ µ.
In vacuum, an exact metric solution satisfies:
Rµν = 0 and R = 0
While our aproximate analytic metric has an error associated with it:
Rµν = O(ɛ) and R = O(ɛ)
Bruno C. Mundim Magnetized Accretion onto Inspiraling BBH 2013-05-23