Consider the for us observable Universe (the entire Universe is many orders larger). It is (I think) common knowledge that the Schwarzschild Radius (SR) exceeds the radius of our observable Universe (extending into the surrounding part of the entire Universe), which can one make conclude that we're living in a black hole.
But if we consider the entire Universe (under the assumption that the entire thing is large scale homogeneous and asymptotically flat), there should by this reasoning co-exist many (an infinity) of these kinds of black holes. At every point in the Universe, there is an SR, larger than the observable space seen from there, surrounding this point.
My question: Is it because of the entire (homogenous) Universe that the black holes like the one we (or creatures on faraway planets) allegedly live in (allegedly) don't exist (the entire Universe obviously can't have an SR).
But if the answer is "No", then what constitutes the singularities in these black holes?