As you approach the event horizon while inside a falling rocket, how does your clock appear to run?

As you approach the event horizon of a black hole while inside a falling rocket, your clock appears to run at a constant, normal rate from your own perspective. This is crucial to understand in the context of general relativity and the effects of gravitational fields.

Within your own reference frame inside the rocket, you experience time as you normally would. The laws of physics, including the passage of time, remain consistent from the perspective of the individual in a local frame of reference. Therefore, your clock would tick normally, and you would not notice any difference in the rate at which time elapses for you while you are falling toward the black hole.

However, this contrasts with how an outside observer would perceive your clock as you approach the event horizon. To someone watching from far away, your clock would seem to run slower as you get closer to the event horizon due to the extreme gravitational time dilation effects. Still, from your own experience inside the rocket, everything feels regular, leading to the conclusion that your clock appears to run uniformly at a normal rate.