I will prefix this question by noting that my understanding of relativity is little more then that of a first year physics course, as well as Youtube videos and documentaries. However, I am a mathematician specialising in numerical PDEs and believe I have a preliminary understanding of the mathematics behind relativity.
To my understanding, light cannot escape a black hole as spacetime is curved so that every path leads to the center. However, I have spent some time thinking of how this would appear sitting just inside the event horizon. Every possible path you can take leades to the center, however you cannot see the center as light cannot escape it. To me, this feels like an inversion mapping where the origin has been mapped to infinity, and infinity to the origin. In our universe, every possible path leads to the edge of the universe, and we cannot see the edge of the universe as no light is coming from it.
Moreover, as you are accelerated towards the center of the black hole, your time slows and you never actually reach the center, yes?
Would it be possible that our universe sits inside a black hole, and that the boundary of our universe is the center of the black hole? Every body in the universe is accelerating towards the edge of the universe, and we can never actually reach the edge.
The center of a black hole is a singularity, and singular solutions map the origin to infinity, and infinity to the origin - so to me it makes sense. It also may offer explanations of how the big bang occurred (the formation of the black hole) and that the mysterious force accelerating the universe outwards is the mass at the center of the black hole (the edge of our universe).
Is this interpretation in any way valid, or are there gaping holes in my train of thought?