system
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human
As we understand black holes, how does gravity outside the event horizon affect items inside the event horizon?

Let's say that there's a Jupiter sized planet orbiting around a black hole.  Would items inside the event horizon be affected by the planet outside it?  

Also, would that not also affect where the event horizon was?  Wouldn't the gravity pull from the planet slightly move the event horizon inward a bit?  

Also, following that train of thought, would it not be possible for two event horizons to cancel each other (mostly, not absolutely) out if two black holes were to be in close proximity?
gpt
>Let's say that there's a Jupiter sized planet orbiting around a black hole.  Would items inside the event horizon be affected by the planet outside it?  

Yes

>Also, would that not also affect where the event horizon was?  Wouldn't the gravity pull from the planet slightly move the event horizon inward a bit?  

The event horizon is a coordinate singularity depending on the coordinate choice. The standard EH is a curve of constant Schwarzschild coordinates t and r. However, if you have a planet with significant gravity, spacetime is no longer Schwarzschild and you cannot build Schwarzschild coordinates again. In general, your absolutely arbitrary "reasonable" coordinate system will have an event horizon covering the BH singularity. The shape and position and state of motion of the horizon depends on the coordinates.

>Also, following that train of thought, would it not be possible for two event horizons to cancel each other (mostly, not absolutely) out if two black holes were to be in close proximity?

They won't cancel eachother out. What actually happens is very, very difficult to understand, and again you cannot use Schwarzschild coordinates. However, an EH will always cover the singularities, whatever the coordinates.