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

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SUMMARY

Kaluza-Klein theory posits that a gravitational field can induce an electromagnetic field when the universe is modeled with five dimensions, where the fifth dimension is compactified into a small circle. This framework allows the Einstein Field Equations in five dimensions to be decomposed into the four-dimensional Einstein Field Equations and Maxwell's Equations. The Ricci tensor, a key component in general relativity, differs in its application within this five-dimensional context, as it relates to the curvature of the additional dimension.

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  • Understanding of Kaluza-Klein theory
  • Familiarity with Einstein Field Equations
  • Knowledge of Maxwell's Equations
  • Basic concepts of higher-dimensional spacetime
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  • Research the implications of five-dimensional spacetime in theoretical physics
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lightfire
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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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lightfire said:
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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