According to our current understanding of physics, attempting to travel through a black hole at faster-than-light (FTL) speeds would not be possible. The theory of general relativity, which describes gravity and the behavior of black holes, suggests that the gravity near a black hole becomes incredibly strong as you approach its event horizon—the point of no return.
As an object approaches the event horizon, the gravitational forces acting on it become infinitely strong. This phenomenon is known as gravitational time dilation, where time slows down significantly as you get closer to the black hole. As a result, it would take an infinite amount of time for an object to reach the event horizon, let alone surpass it and enter the black hole.
Moreover, the concept of FTL travel itself presents significant challenges within the framework of our current understanding of physics. According to Einstein's theory of relativity, the speed of light is considered an ultimate speed limit. As an object with mass accelerates towards the speed of light, its relativistic mass increases, requiring an infinite amount of energy to reach or exceed that limit. These factors make it highly improbable for any physical object, including a ship, to achieve FTL speeds.
However, it's important to note that our understanding of black holes and the nature of spacetime is still incomplete. There are ongoing scientific research and theoretical explorations in the field of physics, such as quantum gravity and string theory, which may provide further insights into the behavior of black holes and the possibilities of FTL travel.