Some Remarks on Gravitational Global Monopoles

Using mainly analytical arguments, we derive the exact relation ${\eta }_{\max }=\sqrt{3/8\pi }$ for the maximal vacuum value of the Higgs field for static gravitational global monopoles. For this value, the global monopole bifurcates with the de Sitter solution obtained for vanishing Higgs field. In addition, we analyze the stability properties of the solutions.