- #1

ChrisVer

Gold Member

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## Main Question or Discussion Point

I was wondering if I can expand the FRW metric in d spatial dimensions, like:

[itex] g_{\mu \nu}^{frw} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & - \frac{a^2(t)}{1-kr^2} & 0 & 0 \\ 0 & 0 & - a^2(t) r^2 & 0 \\ 0 & 0 & 0 & -a^2 (t) r^2 \sin^2 \theta \end{pmatrix} \rightarrow g_{MN} = \begin{pmatrix} g_{\mu \nu}^{frw} & 0 \\ 0 & - 1_{(d-3) \times (d-3)} \end{pmatrix}[/itex]

Or should I insert a ##-a^2 (t) ## for the rest too?

[itex] g_{\mu \nu}^{frw} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & - \frac{a^2(t)}{1-kr^2} & 0 & 0 \\ 0 & 0 & - a^2(t) r^2 & 0 \\ 0 & 0 & 0 & -a^2 (t) r^2 \sin^2 \theta \end{pmatrix} \rightarrow g_{MN} = \begin{pmatrix} g_{\mu \nu}^{frw} & 0 \\ 0 & - 1_{(d-3) \times (d-3)} \end{pmatrix}[/itex]

Or should I insert a ##-a^2 (t) ## for the rest too?