Q:
How do we know that we – and our Solar System – don't live inside a black hole?
A:
There are probably several ways to answer this, but here is one:
From measurements made in the 1920s of the velocities of distant galaxies, it was found that all galaxies are flying away from us at a rate that depends only on their distance from us. No matter which direction we look in the sky this is true. We assume therefore that the Universe is isotropic, meaning rotationally invariant. There is no special or "preferred" direction to space.
Inside a black hole the situation is quite different - all objects are propelled toward the singularity at the center of the black hole. There is a preferred direction in space in the vicinity of a black hole. So, at this time we can say that we do not live inside of a black hole.
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we do not live inside of a black hole
Is there something like a 'center of a black hole'? Particularly going by analogy of Universe being isotropic, there is no center of Universe as we know of.
Do we know anything about beneath the Event Horizon?
Rationalist
The center of a black hole
Yes, it is fair to talk about the center of a black hole, even though it's a mystery about what lies beneath the event horizon, since light cannot escape this region.
CXC