Help me to prove this please

1. Nov 5, 2008

tri3phi

1- Aµναβ=Rµ[να]β ..... prove that the tensor is antisymmetric with respect to indices u and p
2- Denote Sµναβ =Rµ(να)β... prove that the tensor is symmetric with respect to indices u and p
3- if we introduce the spherical coordinate (r,θ,Φ )
X1 =r sin θ cos Φ , X2 =r sin θ sin Φ , X3 =r cos θ
if we denote t=X0 ,show that in these coordinate the asymptotic form of the metric in the linearzed approximation for a massive rotating approximation for a massive rotating source is
ds2 = -(1- 2GM/r)dt2 – (4GJ sin2 θ/r)dt dΦ + (1+(2GM/r))(dr2+ r2 dω2)
dω2 = dθ2 +sin2 θ dΦ2 is a metric on unit round sphere S2 .

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