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Suppose you have the simplest type of black hole - time independent, no angular momentum or charge, Schwarzschild solution, then you modify the situation by adding a stationary mass outside the event horizon (I imagined lowering this slowly on an idealised string).

The question is, does this affect the geometry inside the black hole as well as outside?

My original argument that it didn't relied on my belief that it was impossible to communicate with points arbitrarily close to the event horizon in finite time, which I inferred from the fact that to a remote observer anything appears to take infinite time to reach the event horizon. So if you can't communicate with this thin region around the event horizon, surely you cannot affect anything further in, and presumably that would even include the space time geometry for the entire region inside the event horizon.

Having come to this conclusion, I considered colliding black holes and concluded that, to a remote observer, the geometry from the event horizon down would be indistinguishable from spherically symmetric Schwarzschild right up to the time the event horizons collided. Although this is not what one sees in simulations, this could be because there is inevitable distortion to display things on a plane: the region between the black holes would be very severely warped.

But perhaps I am wrong, and the geometry of the interior of black holes is affected by masses outside. What do the experts say? And if I am wrong, where does the communication argument fall down? Can quantum effects break it? [My argument probably falls down when the thickness of the region around the event horizon is very tiny, as quantum effects probably matter. Especially when it is less than the Planck distance.]

The question is, does this affect the geometry inside the black hole as well as outside?

My original argument that it didn't relied on my belief that it was impossible to communicate with points arbitrarily close to the event horizon in finite time, which I inferred from the fact that to a remote observer anything appears to take infinite time to reach the event horizon. So if you can't communicate with this thin region around the event horizon, surely you cannot affect anything further in, and presumably that would even include the space time geometry for the entire region inside the event horizon.

Having come to this conclusion, I considered colliding black holes and concluded that, to a remote observer, the geometry from the event horizon down would be indistinguishable from spherically symmetric Schwarzschild right up to the time the event horizons collided. Although this is not what one sees in simulations, this could be because there is inevitable distortion to display things on a plane: the region between the black holes would be very severely warped.

But perhaps I am wrong, and the geometry of the interior of black holes is affected by masses outside. What do the experts say? And if I am wrong, where does the communication argument fall down? Can quantum effects break it? [My argument probably falls down when the thickness of the region around the event horizon is very tiny, as quantum effects probably matter. Especially when it is less than the Planck distance.]

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