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During my Master's degree, we studied Black Holes as solutions of Einstein-Maxwell equations, and I was wondering if it would be possible to also add strong or electroweak forces in the classic non-quantum version of General Relativity, i.e. to extend the U(1) electromagnetic symmetry to a non-abelian group SU(N).

I mean, we saw that in a certain way it could be done with the Kaluza-Klein mechanism, but this method has some problems so I don't know if it would be possible in general to find a solution of this kind just by solving the field equations.

What about the same problem in Supergravity?

Aleph12345
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You can definetely add to GR other interactions different from EM.

You just need to be careful on what the meaning (physically intended) of such model is.

For example, QCD is used in order to model the inside of neutron stars, all in the framework of general relativity.

QCD is used to find the equation of state for the matter inside neutron stars, and this solution is feed to Einstein equations in order to study its internal geometry.

This is not like coupling gluons to gravity, tho, since gluons are quantum objects while GR is classical, so you can add other interactions but you must be careful on what you used them for.

LolloBoldo
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