According to our current understanding of black holes based on general relativity, time does not "cease to exist" within a black hole itself, but rather experiences extreme and unusual effects. To explain this concept, we need to consider a few key aspects of black holes.
Black holes are regions of spacetime where gravity is incredibly strong due to the immense concentration of mass within a small volume. The gravitational pull of a black hole is so intense that it creates what is called an event horizon, which is a boundary beyond which nothing, including light, can escape.
When an object crosses the event horizon and falls into a black hole, from an external observer's perspective, time for that object appears to slow down as it approaches the event horizon. This phenomenon is known as gravitational time dilation. As the object gets closer to the black hole's gravitational pull, the strength of the gravitational field becomes increasingly stronger, causing time to pass more slowly for the falling object relative to an observer situated farther away from the black hole.
At the event horizon itself, time dilation becomes infinitely strong. This means that an external observer watching an object falling into a black hole would see the falling object slow down and gradually approach a standstill at the event horizon. From the perspective of the falling object, however, time would appear to pass normally.
Inside the black hole, our current understanding based on general relativity breaks down, and the precise nature of what occurs is still an area of active research and speculation. According to some theories, the gravitational forces within a black hole become so extreme that they cause a singularity, a point of infinite density at the center of the black hole where our understanding of physics breaks down entirely. Within the singularity, our current understanding of space and time may no longer apply.
However, it's important to note that the concept of time ceasing to exist within a black hole is more related to the limitations of our current theories and our inability to describe the behavior accurately. It is an area of active research, and future developments in physics, particularly in the context of reconciling general relativity with quantum mechanics, may provide further insights into the nature of time within black holes.