Find christoffel symbols for metric - ds2 -cos2betadt2 -
ds2 = -cos(2β)dt2 - 2sin(2β)drdt + cos(2β)dr2 + r2dθ2 + r2 sin2θdΦ2
Here β = β(r), Take xo = t, x1 = r, x2 = θ, x3 = Φ
Find christoffel symbols for above metric
i) Γ0 00
ii) Γ0 22
iii) Γ0 33
(iv) Γ0 11
(v) Γ1 11
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ds2 -cos2betadt2 - 2sin2betadrdt cos2betadr2 r2dtheta2 r2 sin2thetadphi2here beta betar take xo t x1 r x2 theta
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