- #1

- 72

- 8

**Homework Statement::**Please see below.

**Relevant Equations::**Please see below.

I am trying to find a reference to a textbook or a paper that details the following time-invariance Kaluza-Klein metric:

\begin{equation}

\mathrm{d}s^2_{(5)}=\lambda_{ab}\left(\mathrm{d}x^a+\omega^{a}_{\phantom{a}i}\mathrm{d}x^i\right)(\mathrm{d}x^b+\omega^{b}_{\phantom{b}j}\mathrm{d}x^j)+\frac{1}{\tau}h_{ij}\mathrm{d}x^i\mathrm{d}x^j.

\end{equation}

So far, I can only find sources for the Kaluza-Klein metric but not it's time-invariant version. Can someone point me to a relevant reference?