If you were to enter a field of localized time dilation caused by a strong gravitational field, it would not give off the illusion of you moving at super speed. Instead, you would experience time passing more slowly compared to someone outside the gravitational field.
In a region with a stronger gravitational field, as predicted by general relativity, time dilation occurs. This means that clocks in this region will appear to run slower compared to clocks located in a region with weaker gravity.
If you were to enter such a region, you would experience time passing more slowly relative to an observer located outside the gravitational field. From your perspective, time would continue to flow at its normal rate, but you would observe clocks outside the field to be running faster. This is often described as time running slower for you relative to the external observer.
However, it's important to note that the experience of time dilation is subjective. You would not perceive yourself moving at super speed or experiencing any change in your own motion. The time dilation effect primarily affects the rate at which time elapses for you compared to an observer in a different gravitational field.
So, while entering a field of localized time dilation would result in a difference in the passage of time compared to observers outside the field, it would not create the illusion of you moving at super speed.