Escape velocity is the ballistic speed required to escape from a gravitational field to infinity, ignoring any third body dynamics. The operative word here being ballistic, meaning unpowered.
In response to prior question removal: The below reference to a Fermi Drive is a tongue-in-cheek handy Gedanken construct for a non-ballistic mechanism. It is not unpublished personal theory. There is no claim of a mechanism to escape a Black Hole.
Now let's suppose I have a Fermi spacecraft with effectively unlimited fuel. This could be via some as yet undefined reactionless drive or a highly efficient ion drive of some kind.
Now the escape velocity from Earth is around 25000 mph, but this is an unpowered ballistic velocity. However I could hop in my Fermi spacecraft and travel at a sedate 50 mph continuously straight up for as long as I like, until I eventually land on the Moon or go elsewhere. Escape velocity is not a factor here because this is a powered ascent not a ballistic one.
Now let's take this same concept to a Black Hole event horizon.
I can sedately and continuosly travel for as long as I like. I don't have to deal with super luminal escape velocities.
So where does this leave me? Can I escape from a Black Hole, or am I running up against Lorentz contractions in time or some such rather than escape velocity issues?
Fermi Drive - Patent Pending ☺