Static spherically symmetric solutions of the SO(5) Einstein Yang–Mills equations

Abstract

Globally regular (i.e., asymptotically flat and regular interior) spherically symmetric and localized (“particlelike”) solutions of the coupled Einstein Yang–Mills (EYM) equations with gauge group SU(2) have been known for more than 20 years, yet their properties are still not well understood. Spherically symmetric Yang–Mills fields are classified by a choice of isotropy generator and SO(5) is distinguished as the simplest gauge group having a model with a non-Abelian residual (little) group, SU(2)×U(1), which admits globally regular particlelike solutions. We exhibit an algebraic gauge condition which normalizes the residual gauge freedom to a finite number of discrete symmetries. This generalizes the well-known reduction to the real magnetic potential w(r,t) in the original SU(2) YM model. Reformulating using gauge-invariant polynomials dramatically simplifies the system and makes numerical search techniques feasible. We find three families of embedded SU(2) EYM equations within the SO(5) system, one of which was first detected only within the gauge-invariant polynomial reduced system. Numerical solutions representing mixtures of the three SU(2) subsystems are found, classified by a pair of positive integers.