Hi I am using the metric [itex]ds^{2}=c^{2}dt^{2}-a^{2}(t)[\frac{dr^{2}}{1-kr^{2}}+r^{2}(dθ^{2} + sin^2θd^{2}∅)[/itex]](adsbygoogle = window.adsbygoogle || []).push({});

and am subsequently trying to derive the christoffel symbols:

[itex]\Gamma^{\sigma}_{\mu\nu}=\frac{1}{2}g^{\sigma\rho}(\partial_{\nu}g_{\rho\mu} +\partial_{\mu}g_{\rho\nu} -\partial_{\rho}g_{\mu\nu})[/itex]

I am stuck with finding these and would like some help for instance why does [itex]\Gamma^{0}_{11}=\frac{a\dot{a}}{c(1-kr^{2}}[/itex] where does the c come from?

I understand that one substitutes in the numbers but when attempting this i dont fully understand the differential but for instance:

[itex] \partial_{0}=g_{11}[/itex] is this basically [itex] \frac{\partial}{\partial t}a^{2}\frac{dr^{2}}{1-kr^{2}}[/itex]? and if so are all differentials with numbers greater than 0 just = 0 then i.e what would [itex] \partial_{2}[/itex] be equal to?

I appreciate any help

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# Tips for deriving the friedmann equations

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