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Metric ansatz:

[itex]

ds^{2} = e^{\tilde{A}(\tilde{\tau})} d\tilde{t} - d\tilde{r} - e^{\tilde{C}(\tilde{\tau})} dΩ

[/itex]

where: [itex]d\tilde{r} = e^{\frac{B}{2}} dr[/itex]

Metric tensor:

[itex]g_{μv}=diag (e^{\tilde{A}(\tilde{\tau})}, -1,- e^{\tilde{C}(\tilde{\tau})}, - e^{\tilde{C}(\tilde{\tau})} sin^2 θ ) [/itex] correct?

Christoffel Symbols:

[itex]\Gamma^{μ}_{vρ}=\frac{1}{2}g^{μλ}(∂_{v}g_{ρλ}+∂_{ρ}g_{μλ}-∂_{λ}g_{vρ})[/itex]

[itex]\Gamma^{0}_{00}=\frac{1}{2}g^{00}(∂_{0}g_{00}+∂_{0}g_{00}-∂_{0}g_{00})[/itex]

[itex]\Gamma^{0}_{00}=\frac{1}{2}g^{00}(∂_{0}g_{00})[/itex]

[itex]\Gamma^{0}_{00}=\frac{1}{2}e^{-\tilde{A}(\tilde{\tau})}(\frac{∂}{∂\tilde{t}}e^{\tilde{A}(\tilde{\tau})})[/itex]

[itex]\Gamma^{0}_{00}= 0[/itex] correct?

[itex]\vdots[/itex]

etc

And:

[itex]\frac{∂}{∂\tilde{r}}e^{\tilde{A}(\tilde{\tau})}= 0 [/itex] correct?

What is the difference between:

[itex]\tilde{t}[/itex] and [itex]\tilde{\tau}[/itex] ?

[itex]{r}[/itex] and [itex]\tilde{r}[/itex] ?

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# Calculate Christoffel Symbols

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