Others are telling me the Einstein Field Equations can work in other dimensions other than 4D (3D space + 1D time). How true is it? So I'd like to ask for clarifications. I googled about it and found one reference for example:
Kaluza–Klein theory - Wikipedia
I assume the Einstein equations is...
The ansatz for the 5D metric is
\begin{equation}
G_{\mu \nu}= g_{\mu \nu}+ \phi A_{\mu} A_{\nu},
\end{equation}
\begin{equation}
G_{5\nu} = \phi A_{\nu},
\end{equation}
\begin{equation}
G_{55} = \phi.
\end{equation}
This information was extremely enlightening for me, but what's the analogous...
From time to time, I point to string theoretists that they should have considered more seriously to use Kaluza-Klein theory and they invariably answer me "we do", and move forward. So I am starting to thing that perhaps I am wrong and I have missed some developing of the theory the the XXIth...
Can Kaluza-Klein theory accommodate magnetic charge? If so is there a simple geometric difference between electric and magnetic charge in such a theory?
Thanks!
Does any know how to perform Kaluza-Klein reduction via mathematica? The task becomes very tedious if the job is done manually when successive reductions are done.
http://en.wikipedia.org/wiki/Kaluza–Klein_theory
##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche)
http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf (this author makes some interesting arguments)
Also, a lot (if not all...
I know this is technically not orthodox GR, but it is closely related. I was reading about Kaluza-Klein theory, but I don't completely understand it. Under what circumstances would could a gravitational field induce an electromagnetic field under this theory. Also, how is the Ricci tensor different?
In Kaluza-Klein theory one introduce an extra fifth spatial dimension, to the usual four-dimensional manifold ##M^4## in General Relativity called space-time. This extra dimension has a symmetry; i.e. it is spanned by a Killing vector and it's taken to be compact. One views this extra dimension...
I'd never heard of Kaluza-Klein theory before today, and from what I've read I think that's rather odd. Taking it from a purely non-quantum, relativistic unification of gravity and electromagnetism, what's wrong with it? I know it has been subsumed into other, more sophisticated theories, but on...
In Kaluza-Klein theory, the gauge symmetries for all the fundamental
forces are mapped onto the higher spatial dimensions.
So the internal symmetries are now externalised.
Does this imply that you can extend the analogy with gravity further:
so for example, if the 5th dimension contains...