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Suppose you have a non-charged, non-spinning, spherically symmetric super massive black hole. Suppose also you could manipulate a sizable mass distribution within 10% of the Schwarzchild radius outside of the event horizon. Attached to that mass distribution is a device that can measure changes in the Black Hole's gravitation filed.

How fast can the detector detect responses from the black hole due to fluctuations in the manipulated matter?

I have a few guesses:

For the following assume the "duration of perturbation" referred to is on the order of the Compton Wavelength of the Black Hole divided by the speed of light.

A) Information redundancy Scenario/Negligible Event Horizon Information Use. This is a highly symmetric scenario. The information of mass distribution is not only stored on the surface of the black hole, it's uniform throughout the Event Horizon. In principle, especially taking into account possible entanglement scenarios, the "kickback signal" of the black hole due to the manipulated mass will take as much time to get back to the detector as the gravitational wave took to be sent, plus the duration of whatever perturbations occur. Time detection, roughly (20% of the Schwarzchild Radius/c) For a super massive black hole, this would be faster than the gravitational waves from the manipulated mass can even reach the center of the black hole.

B) Response Effectively ignores Event Horizon: Gravitational Waves from the manipulated mass generate no kickback until sufficient time has allowed them to reach the center of the black hole and a response to return. These perturbations take the same amount of time to allow detection of a response. Mass manipulated in the center can't alter information at the Event Horizon faster than the speed of information. This still means there has not been sufficient time for the detector to have received information from everywhere on the Event Horizon.

C) There is no redundancy in the information in the Event Horizon: No complete response from the black hole can be detected until pulses from the manipulated mass have had time to reach the entirety of the event horizon and then send a response. However close the detector is to the event horizon, full information of the response from the black hole will take at least (four times the Schwarzchild radius)/c to reach the detector even though first encountering a response begins at (twice the schwarzchild radius)/c.

I believe A and B might imply some faster than light information transferal.

R. Romero
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    Maybe I misunderstand what you're saying, but your question seems to imply that we can perform some action outside the event horizon and get some response to that action from the interior of the black hole. But no information about the interior can cross the event horizon. Once matter crosses the EH it can no longer change the local spacetime curvature, the effect it has on the curvature as it falls in get effectively frozen. See http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html – PM 2Ring Oct 22 '18 at 16:09
  • I think only scenario B requires information to come from within. I am confused on if information can escape. Suppose there is the initial collapse forming the black hole. It starts off with some Schwarzchild Radius. Eons later I look at the same black hole and I've found an increase in its radius. I can know that its mass has increased a certain fairly specific amount, right? And mass has accumulated at the center? Im assuming I can measure the radius of the black hole, perhaps even the rate of increase of its Event Horizon. I'm admit i'm only halfway through Schutz. – R. Romero Oct 22 '18 at 16:19
  • We can assume mass somehow accumulates at the centre, but we can't really talk about it sensibly until we have a theory of quantum gravity. In pure (non-quantum) GR, anything that crosses the EH soon (in its proper time) hits a singularity. Crudely speaking, if the spacetime manifold is like a 4D sheet of graph paper, the singularity is a spacelike line missing from the graph paper, there's not even empty space there. – PM 2Ring Oct 22 '18 at 16:36
  • Ben Crowell explains that last point better than I do: https://physics.stackexchange.com/a/391183/123208 – PM 2Ring Oct 22 '18 at 16:46
  • Thanks for the link!

    Without a quantum theory of gravity, can we know for sure certain particulars of the interior can't escape? Suppose a response was detected on the time scale associated with scenario B, what minimal changes would have to happen to GR to account for that?

    On thinking about it, I'm assuming Scenario C is the current notion of the time scale of response of a black hole? That's the one where detection requires information from the entirety of the Event Horizon.

     – R. Romero Oct 22 '18 at 17:36

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