Questions about Kaluza-Klein Theory

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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?
 
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PeterDonis
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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.
 

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