Help with identifying a reference for the time-invariant Kaluza-Klein metric

In summary, the conversation is about finding a reference for the time-invariant Kaluza-Klein metric, specifically in textbooks or papers. The person asking has already checked books by Joseph Polichinski, GWS green books, and Kaku's books, but could not find the relevant information.
  • #1
user1139
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?
 
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  • #2
I guess you tried the classical books on M-theory and Superstring of Joseph Polichinski, GWS green books or Kaku's books. (mind you, Kaku has also popular books but I am referring to his technical books).
Have you?
 
  • #3
Yes @MathematicalPhysicist I have perused Polichinski's book in particular and could not find a mention of the time-invariant Kaluza-Klein metric.
 

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