How do we know that we â€“ and our Solar System â€“ don't live inside a black hole?
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.