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Let's say I'm orbiting a black hole at a great distance. Then something happens. On the far side of the black hole, a neutron star of significant mass merges with my black hole.

Will I ever know it happened? Will I ever detect an increase in my black hole's mass? If I do, doesn't that mean I received information from my black hole?

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The No-hair theorem states that Black Holes have only three externally detectable properties and are characterized by them. They are the mass, angular momentum and charge of the Black Hole. So technically, you can detect them. So yes, you will know it happened and it wouldn't be in violation of any known laws.

(If you let a body free fall under the Black Hole's gravitation field and measure its acceleration at a certain distance, and then remeasure the acceleration at the same distance after the Neutron Star falls into the Black Hole, you will detect a difference.)

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    $\begingroup$ I've read that the No-hair theorem only applies to stationary states--this book also mentions that "perturbation calculations of spherical collapse, suggest that black holes will settle down to a stationary state", but I imagine this is only in some limit of sufficient time after any new matter has fallen into the black hole. So for some suitably short time you might be able to detect other characteristics of the infalling body from gravitational waves besides just its contribution to the final mass/angular momentum/charge. $\endgroup$ – Hypnosifl Feb 2 '15 at 1:15
  • $\begingroup$ but I think since the question deals only with mass increase, the no hair theorem is okay here. thanks for letting me know though, I'll read into that.. $\endgroup$ – Hritik Narayan Feb 2 '15 at 4:43
  • $\begingroup$ At which speed will the spacetime distorsion change propagate from the black hole? $\endgroup$ – dan Mar 1 '17 at 17:49
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I guess you would, I mean you are orbiting around it because you can feel the gravitational field, therefore a change in mass and hence in the field should be measurable. The last question escapes a little my knowledge, but from the same argument as before, yes you probably would have received information from the black hole.

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What Hritik Narayan said is true. But I think your questions is more of a "why is it true"? Here is my understanding in very layman's terms :)

Matter tells space how to curve, while space tells matter how to move.
So, matter, including black holes, curves space, thus creating gravity and causing other matter to "fall" or to move in that curved space. So, even though no information can escape from the black hole, the space curvature outside of the black hole is what you are seeing when are talking about its gravity.

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Let's say you are orbiting a black hole, and some other black hole comes in 'you - your black hole' system, your will for sure notice it:

1: If the incoming black hole is of mass comparable to your black hole, the system now have a new entity in it which for sure will change your trajectory significantly around original black hole.

2: As they merge, the mass of new black hole at that point in space will increase which in turn will create a bigger gravitational well and a bigger range of event horizon. your speed will increase around the new black hole.

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