If we start with the Einstein-Hilbert action with no matter, and consider time independent finite energy field configurations, then any static solution (e.g Schwarzchild metric) seems to be a soliton-like solution of the equations of motion corresponding to the Lagrangian.
Now topological solitons have the property that perturbative quantum fluctuations don't decay solitons to trivial ground state configurations, i.e they are topologically protected (I don't know whether something like this which prevents decay from solitonic configuration to the ground state configuration is true of non-topological solitons). However in the case of black holes, Hawking radiation processes decay the black hole metric to flat space metric.
Considering the two viewpoints, can static black hole configurations be considered as solitonic configurations? If yes, how is the doubt in the second paragraph resolved?