Could you expand a bit more on it being “geometrically impossible”? As in, what makes it so? Is it just how the math works out, that standing still or escaping such bent spacetime would require infinite amounts of energy?

Why can’t anything escape from inside a black hole? I hear that it’s because “escape velocity is equal to the speed of light” but an object dosent have to exceed the escape velocity to escape the objects gravitational pull. I’m wondering if it’s a physics problem (in that some physical law is stopping us) or an engineering problem (in that it’s just difficult to imagine a system that could output enough energy to counteract the pull).