^
OK, I feel that there is something wrong with it. Can you check it with your Mathematica?
Also, there other non-zero Gammas which I haven't mentioned.
So far we have computed only 4 Gammas:
\Gamma^{r}_{rr}=\dfrac{-rB}{(Br^2 -1)}
\Gamma^{\theta}_{\theta r }=\dfrac{1}{r}
\Gamma^{\phi}_{\phi r}=\dfrac{1}{r}
\Gamma^{\phi}_{\phi \theta} = \dfrac{1}{\tan \theta}
Another one:
\Gamma^{r}_{\theta \theta}=-r(Br^2-1)...
\dfrac{d^2 x}{dt^2}=-\nabla \Phi
\dfrac{d^2 x^\mu}{d\tau^2}= -\Gamma^{\mu}_{\alpha \beta}{}\dfrac{dx^\alpha}{d\tau}\dfrac{dx^\beta}{d\tau}
These two equations, to be true, the way they are written should ring a bell. They are similar yet not identical. What is the meaning behind them...
Peter, I calculated Einstein Tensor, please check if it is correct:
G_{\mu \nu}=\left [ \begin{matrix}
\dfrac{6 G M (2 M - r)}{r R^3}& 0 & 0 & 0 \\
0 & \dfrac{2 M (-G r^3 + R^3)}{(2 M - r) r^2 (2 G M r^2 - R^3)} & 0 & 0 \\
0 & 0 & \dfrac{-((M (M - r) (2 G (3 M - r)...