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Globally regular (ie. asymptotically flat and regular interior), sphericallysymmetric and localised ("particle-like") solutions of the coupled EinsteinYang-Mills (EYM) equations with gauge group SU(2) have been known for more than20 years, yet their properties are still not well understood. Sphericallysymmetric Yang--Mills fields are classified by a choice of isotropy generatorand SO(5) is distinguished as the simplest model with a \emph{non-Abelian}residual (little) group, $SU(2)\times U(1)$, and which admits globally regularparticle-like solutions. We exhibit an algebraic gauge condition whichnormalises the residual gauge freedom to a finite number of discretesymmetries. This generalises the well-known reduction to the real magneticpotential $w(r,t)$ in the original SU(2) YM model. Reformulating using gaugeinvariant polynomials dramatically simplifies the system and makes numericalsearch techniques feasible. We find three families of embedded SU(2) EYMequations within the SO(5) system, one of which was first detected only withinthe gauge-invariant polynomial reduced system. Numerical solutions representingmixtures of the three SU(2) sub-systems are found, classified by a pair ofpositive integers.

Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations