Kaluza-Klein Theory Q&A: Inducing EM Field & Ricci Tensor

[lightfire]

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?

 

[jedishrfu]

Wikipedia has a writeup on it that may answer some questions at historically:

http://en.wikipedia.org/wiki/Kaluza–Klein_theory

 

[PeterDonis]

Under what circumstances would could a gravitational field induce an electromagnetic field under this theory.

Under the circumstance that the universe has five dimensions, not four, and the fifth dimension is curled up into a tiny circle at each point of what we call four-dimensional spacetime. Then the Einstein Field Equation for "gravity" in five dimensions can be split up into two pieces: one is the Einstein Field Equation for gravity in four dimensions; the other turns out to be Maxwell's Equations for electromagnetism in four dimensions.