While the singularity of the BB is in the past, the singularity of the black hole is in the future.No. The characteristic of black holes is that the singularity is in the future, and, by definition, nothing can escape the event horizon (except, possibly, Hawking radiation).
The singularity of the big bang is in the past. If anything, it was more like a white hole, the time reversal of a black hole, except it was not embedded in some outer spacetime into which it ejected its contents.
As the physics student correctly pointed out in the video of post #172 the mathematics predicts inside the event horizon space takes on properties of time and time takes on properties of space.
This can be explained using the light cones in a Minkowski space-time diagram.
As an object moves towards the event horizon the light cones narrow as the object approaches the speed of light.
When it passes the event horizon it "tips over" which can be explained by examining the Schwarzschild metric.
This is the metric as an exterior solution of the Einstein's field equations outside the event horizon.
All metrics for space-time are defined as having a positive coefficient for the time-like dt term and a negative coefficient for the space-like dr term.
When r < 2MG/c² which is an interior solution inside the horizon, the signs are interchanged and the time like term becomes space-like and vice versa.
This is geometrically equivalent to rotating the axes 90º.
The object reaches the singularity in the future hence the singularity is in the objects future light cone.
This is all well and good except if the object wants to escape the black hole it has to change direction and move away from the singularity but to do this it will have to travel backwards in time into the past since the space-like and time-like regions have been interchanged.
This is a problem putting it mildly if the BB originated from a supermassive black hole where the singularity of the universe and the black hole were one in the same thing, expansion can only occur into the universes' past.
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