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## Main Question or Discussion Point

This is a question inspired by the "Golf Ball" thread, which is no longer open for comments, I guess.

For a black hole of constant mass, the metric external to the black hole can be written in Schwarzschild metric, which is characterized by the constant [itex]M[/itex], and the corresponding radius [itex]2 M G/c^2[/itex]. What I'm wondering is whether in a situation where there is a tiny (compared to the mass of the black hole) stream of mass falling into the black hole, is it a good approximation to the time-dependent external metric to simply replace [itex]M[/itex] by [itex]M(t)[/itex]? Or would the effect of infalling matter make a more complicated change to the metric?

For a black hole of constant mass, the metric external to the black hole can be written in Schwarzschild metric, which is characterized by the constant [itex]M[/itex], and the corresponding radius [itex]2 M G/c^2[/itex]. What I'm wondering is whether in a situation where there is a tiny (compared to the mass of the black hole) stream of mass falling into the black hole, is it a good approximation to the time-dependent external metric to simply replace [itex]M[/itex] by [itex]M(t)[/itex]? Or would the effect of infalling matter make a more complicated change to the metric?