According to our current understanding of black holes based on general relativity, it is not possible to pull someone out of a black hole once they have crossed the event horizon. The concept of the event horizon is crucial in understanding black holes—it is the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole.
The immense gravitational force near the event horizon of a black hole is such that any object, including a person or a rope, would be stretched and torn apart by a process known as spaghettification. This happens due to the extreme tidal forces that arise from the steep gravitational gradient near the black hole.
While a powerful rocket may generate an enormous amount of thrust, it would not be able to overcome the intense gravitational pull of a black hole. In fact, as an object approaches the event horizon, it would require an infinite amount of energy to escape the black hole's gravitational grip.
It's important to note that our understanding of black holes is based on general relativity, and their behavior in the presence of quantum effects is still an active area of research. In certain hypothetical scenarios involving quantum gravity or yet-to-be-understood physics, some scientists speculate that there might be mechanisms for objects to escape a black hole. However, these ideas remain purely theoretical and are far from being established or testable at present.
In summary, based on our current understanding of black holes, it is not feasible to rescue someone who has crossed the event horizon using a powerful rocket or any other means. The extreme gravitational forces near the event horizon make escape impossible according to our current understanding of physics.