Are the boundaries of a black hole, the event horizon, similar to the boundary at the end of our observable universe?
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Both the black hole horizon and the cosmological horizon are considered event horizons. So in that way, yes they are similar. Any information crossing the black hole horizon is just as lost to us as information crossing our cosmological horizon. However, they are not entirely similar. An observer crossing our cosmological horizon may still turn around and begin moving in the other direction. They will never reach us but they may reach a point that is currently within our observable universe. Alternatively, an observer crossing the event horizon of a black hole is bound inexorably toward the singularity. They may never turn around and move in the other direction because to them, all directions point to the centre of the black hole.
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$\begingroup$ thank you, you explained this very well and I understand what you have said. If I was up on my GR I'd research it more, but thank you. $\endgroup$– BudnpkCommented Jan 27, 2014 at 1:21
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$\begingroup$ One small comment regarding your statement :"bound inexorably toward the singularity.. [and so on]", try reading the final conclusions from this paper "On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses" jstor.org/stable/1968902 , as to why there are is no "Schwarzschild singularity" in a system with many gravitating masses such as our universe. $\endgroup$– Mihai B.Commented Feb 25, 2017 at 8:04