It is striking how people are trying to apply the theories outside of their domain. Your question asks about the Schwartzshield's solution to the General Relativity equations, which is by definition unchanging and eternal. Yet, it is known, that any black hole has a finite lifetime defined by its evaporation.

What result are you expecting by trying to draw any conclusions from a purely mathematical solution and extrapolating its conditions to the timespans to which it is known the model is unapplicable?

It is striking how people are trying to apply the theories outside of their domain. Your question asks about the Schwartzshield's solution to the General Relativity equations, which is unchanging and eternal. Yet, it is known, that any black hole has a finite lifetime defined by its evaporation.

What result are you expecting to derive by trying to draw any conclusions from a purely mathematical solution and extrapolating its conditions to the timespans to which it is known the model is unapplicable?