Spatially Compact Solutions and Stabilization in Einstein-Yang-Mills-Higgs Theories

New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet resp. doublet representation are presented. They form continuous families parametrized by $\alpha=M_W/M_Pl$ ($M_W$ resp. $M_Pl$ denoting the W-boson resp. the Planck mass). The corresponding spacetimes are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as $\alpha$ increases (for the triplet) or decreases (for the doublet).