An object which passes the event horizon needs a finite proper time for this. But an infinitely far observer wouldn't see that the object passes the event horizon. But if the observer doesn't see this, would he be able to recognize the increase of mass, charge and angular momentum of the black hole? With the increasing mass of the black hole also the Schwarzschild radius will increase, how can the observer interpret this?
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$\begingroup$ Essentially a duplicate of How can anything ever fall into a black hole as seen from an outside observer? $\endgroup$– ACuriousMind ♦Oct 28, 2015 at 18:01
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1$\begingroup$ To an infinite observer the separation between the two masses doesn't make any difference, neither classically nor in general relativity. They would always see the combined mass-energy of the entire gravitating structure. $\endgroup$– CuriousOneOct 28, 2015 at 18:01
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The no hair theorem (that sufficiently symmetric systems that don't change in time ate characterized by their charge, angular momentum and energy) is purely about a time independent system.
Essentially that means that as time goes on you can get closer and closer to one of those systems.
So if you approach a black hole event horizon people on the outside can see the combination of original black bole plus new thing falling in look more and more like a combined system of possibly different charge (if the in fall has charge), possibly different energy (if the in fall has some effective energy), and possibly different angular momentum (if the in fall has some effective angular momentum).
