Those are great questions.
The first one is over my head, though I know that the answer is that static fields do extend out from black holes. Of course, before the black hole forms the charge and its field are already there, so the field doesn't really have to propagate, just stay put. If we get a better answer, we'll update.
On the second question, the answer is yes. That makes the General Relativity equations fundamentally non-linear, which leads to their weird behavior. On the other hand, in some ways it leads to more boring behavior. Imagine two big stars in strongly elliptical orbit around their center of mass. As they move closer together, gravitational potential energy is lost and kinetic energy is gained. If only one of those two counted as a source term from gravity, the effective mass as measured from the distant gravity would oscillate up and down. Since it doesn't, they most both in effect count.
Mike W.
(published on 12/28/2009)
