As an object approaches the event horizon of a black hole, the gravitational time dilation becomes more and more extreme. However, it's important to note that from an observer's perspective, it would take an infinite amount of time for an object to reach the event horizon.
According to general relativity, as an object approaches the event horizon of a black hole, the gravitational time dilation experienced by that object approaches infinity. This means that time appears to slow down more and more as one gets closer to the event horizon from an external observer's point of view.
However, as the object approaches the event horizon, its own perception of time remains normal. In other words, an object falling into a black hole will not notice any significant change in its own passage of time until it reaches the singularity at the center.
It's important to remember that our current understanding of physics breaks down at the singularity of a black hole, and the extreme conditions near the event horizon are not fully understood. Therefore, while the time dilation becomes more significant as an object approaches the event horizon, the exact limit of time dilation at the event horizon itself is not well defined within our current understanding of physics.