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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?

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  • $\begingroup$ I suppose you can couple any matter theory to the Einstein Hilbert at the classical level; perhaps this is my ignorance, but can non-abelian gauge theories be interpreted as classical matter? $\endgroup$
    – Integral fan
    Commented Jun 7 at 17:43
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    $\begingroup$ There are plenty of so called “hairy black holes” solutions for classical Einstein-Yang-Mills and Einstein-Yang-Mills-Higgs field equations. However, such solutions would not necessarily correspond to black holes in quantum theories with non-abelian gauge fields. $\endgroup$
    – A.V.S.
    Commented Jun 7 at 18:29
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    $\begingroup$ Of possible interest - Black hole characteristics beyond mass, charge, spin? $\endgroup$
    – mmesser314
    Commented Jun 7 at 19:14

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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.

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  • $\begingroup$ Sorry with "QCD" do you mean Quantum Chromodynamics on a fixed curved spacetime, or do you mean General Relativity with a SU(3) global group? $\endgroup$
    – Aleph12345
    Commented Jun 7 at 18:43
  • $\begingroup$ Quantum chromodynamics on a curved, fixed background $\endgroup$
    – LolloBoldo
    Commented Jun 7 at 18:45
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    $\begingroup$ Namely GR with a $SU(3)$ gauge-invariant matter component $\endgroup$
    – LolloBoldo
    Commented Jun 7 at 18:46
  • $\begingroup$ Do you have a reference for such a neutron star model? $\endgroup$
    – Integral fan
    Commented Jun 7 at 18:46
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    $\begingroup$ inspirehep.net/literature/1610263 and inspirehep.net/literature/839461 are the first i have found, but there is plenty of literature on that on inspirehep $\endgroup$
    – LolloBoldo
    Commented Jun 7 at 19:00

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