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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?

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    One correction: as you fall toward the center of the black hole, assuming the simplest case of a nonrotating black hole, you reach the singularity in finite proper time -- that is, in finite time on your own clock. – Chiral Anomaly Oct 28 '20 at 23:21
  • Hmmm, well that is a gaping hole then. It raises the question of what it means to reach the singularity though. Are you crushed into a point, or is space it self converging? –  Oct 28 '20 at 23:32
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    You are crushed into a point, because all timelike worldlines inside the horizon terminate at the singularity in finite proper time, and all points on your body follow timelike worldlines. By the way, the (mathematical) existence of the singularity is interpreted as a clue that general relativity is only an approximation and that we are pushing it beyond the limits of its validity, the same way we interpret most singularities in physics. What really happens near the center of a black hole probably can't be answered without the help of quantum physics, and AFAIK it's still an open question. – Chiral Anomaly Oct 29 '20 at 00:24
  • You may enjoy reading what Ben Crowell has to say about black hole singularities in pure GR (i.e., without quantum corrections) in this extensive answer. The singularity isn't in the past lightcone of any observer, so in a sense it doesn't exist until you get there. We expect that quantum corrections to GR don't become significant until much smaller than the atomic scale, perhaps near the Planck length. – PM 2Ring Oct 30 '20 at 05:02

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