The concept you're referring to, often associated with science fiction, is known as "warp drive." It involves creating a bubble or warping of spacetime that allows for faster-than-light travel. While this idea has been explored in theoretical physics, it is still highly speculative, and the feasibility of constructing a warp drive remains uncertain.
According to our current understanding of general relativity, objects with mass cannot exceed the speed of light in a vacuum. The region around a black hole, called the event horizon, represents a boundary beyond which nothing, including light, can escape due to the immense gravitational pull of the black hole. Since the warp drive concept relies on warping spacetime, it is unclear how it would interact with the extreme curvature of spacetime near a black hole.
The behavior of spacetime near the event horizon is highly complex, involving intense gravitational effects and time dilation. Theoretical studies on warp drives and black holes suggest that attempting to use a warp drive to escape from inside the event horizon would likely encounter significant obstacles and paradoxes. These may include extreme tidal forces, the need for exotic matter with negative energy densities (which has not been observed), and potential violations of causality.
It's important to note that our current understanding of physics is limited, and new discoveries or advancements may offer insights that could change our understanding of these concepts. However, as of now, using a warp drive to escape from within the event horizon of a black hole remains purely speculative and not supported by established scientific theories.