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.