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?
 
Physics news on Phys.org
  • #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.
 

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

What is the Kaluza-Klein theory?

The Kaluza-Klein theory is a classical unification scheme that attempts to unify gravity and electromagnetism by extending general relativity to a five-dimensional spacetime. The extra dimension is typically compactified or curled up in such a way that it is not observable at low energies.

What is a time-invariant Kaluza-Klein metric?

A time-invariant Kaluza-Klein metric is a specific form of the metric in Kaluza-Klein theory that does not explicitly depend on time. This implies that the metric components are functions of the spatial coordinates and possibly the extra dimension but remain constant over time.

How can I identify a reference for the time-invariant Kaluza-Klein metric?

To identify a reference for the time-invariant Kaluza-Klein metric, you can start by reviewing foundational papers and textbooks on Kaluza-Klein theory. Key references include works by Theodor Kaluza and Oskar Klein, and more recent reviews in higher-dimensional theories and string theory literature. Searching academic databases like Google Scholar, arXiv, and using keywords related to "time-invariant Kaluza-Klein metric" can also be helpful.

What are some key papers or books on Kaluza-Klein theory?

Some key papers include Theodor Kaluza's original 1921 paper "Zum Unitätsproblem der Physik" and Oskar Klein's 1926 paper "Quantum Theory and Five-Dimensional Theory of Relativity." Important books include "Modern Kaluza-Klein Theories" edited by T. Appelquist, A. Chodos, and P.G.O. Freund, and various sections in string theory textbooks like "String Theory" by Joseph Polchinski.

How does the time-invariant assumption simplify the Kaluza-Klein metric analysis?

The time-invariant assumption simplifies the analysis of the Kaluza-Klein metric by reducing the number of variables that the metric components depend on. This can lead to simpler differential equations and facilitate finding exact solutions. It also often aligns with physical scenarios where the extra dimensions are considered static or evolve on timescales much longer than the observable universe.

Similar threads

Replies
4
Views
2K
Replies
5
Views
3K
Replies
3
Views
2K
Replies
3
Views
2K
Replies
13
Views
2K
Replies
12
Views
2K
Replies
16
Views
3K
Replies
2
Views
3K
Replies
1
Views
1K
Back
Top