### 3.9 Gauged boson stars

In 1988, Bartnik and McKinnon published quite unexpected results showing the existence of particle-like
solutions within Yang–Mills coupled to gravity [20]. These solutions, although unstable, were
unexpected because no particle-like solutions are found in either the Yang–Mills or gravity sectors in
isolation. Recall also that no particle-like solutions were found with gravity coupled to electromagnetism in
early efforts to find Wheeler’s geon (however, see Section 6.3 for discussion of Ref. [70], which finds geons
within AdS).
Bartnik and McKinnon generalize from the Abelian gauge group to the non-Abelian
group and thereby find these unexpected particle-like solutions. One can consider, as does Ref. [194] (see
Section IIp), these globally regular solutions (and their generalizations to for ) as gauged
boson stars even though these contain no scalar field. One can instead explicitly include a scalar field
doublet coupled to the Yang–Mills gauge field [39] as perhaps a more direct generalization of the ()
charged boson stars discussed in Section 3.3.

Ref. [74] studies BSs formed from a gauge condensate of an gauge field, and Ref. [41] extends
the Bartnik–McKinnon solutions to conformal gravity with a Higgs field [41].