3.9 Gauged boson stars

In 1988, Bartnik and McKinnon published quite unexpected results showing the existence of particle-like solutions within SU (2) 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. [70Jump To The Next Citation Point], which finds geons within AdS).

Bartnik and McKinnon generalize from the Abelian U (1 ) gauge group to the non-Abelian SU (2) 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 SU (n) for n > 2) 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 (U(1)) charged boson stars discussed in Section 3.3.

Ref. [74] studies BSs formed from a gauge condensate of an SU (3) gauge field, and Ref. [41Jump To The Next Citation Point] extends the Bartnik–McKinnon solutions to conformal gravity with a Higgs field [41].

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