  Spontaneous global symmetry breaking of O(3) scalar field gives rise to
point-like topological defects, global monopoles. By taking into account
self-gravity,the qualitative feature of the global monopole solutions depends
on the vacuum expectation value v of the scalar field. When v < sqrt{1 / 8 pi},
there are global monopole solutions which have a deficit solid angle defined at
infinity. When sqrt{1 / 8 pi} <= v < sqrt{3 / 8 pi}, there are global monopole
solutions with the cosmological horizon, which we call the supermassive global
monopole. When v >= sqrt{3 / 8 pi}, there is no nontrivial solution. It was
shown that all of these solutions are stable against the spherical
perturbations. In addition to the global monopole solutions, the de Sitter
solutions exist for any value of v. They are stable against the spherical
perturbations when v <= sqrt{3 / 8 pi}, while unstable for v > sqrt{3 / 8 pi}.
We study polar perturbations of these solutions and find that all
self-gravitating global monopoles are stable even against polar perturbations,
independently of the existence of the cosmological horizon, while the de Sitter
solutions are always unstable.
