A familiar scenario in scifi: a bubble of space is isolated artificially from the outside world by means of time dilation: time inside the bubble moves more slowly than time outside it. Assume that the boundary is blurred. Time dilation gradually increases as you approach the center. This is similar to time dilation caused by gravity. Also assume time at the center does not stop but is simply the slowest.
There is an object which lies inside the bubble and we attempt to move it (edit: The bubble is small enough so that someone from the outside may attempt to move it using a tether or a rod). From our perspective, our action may appear normal. From the object's perspective we move it faster than we intend to. That raises a question: by moving that object, do we experience more inertia as if the object was more massive? Does time dilation make us perceive that the object in the bubble is more massive than its classical mass?
A second effect is light crossing the bubble: light hitting the bubble's boundary at an incident (non perpendicular) angle, will have the wave nearer to the bubble's center move more slowly. Will that cause light to diffract? The reason light diffracts when crossing a prism is the slower light speed within the prism, and that's what defines the refractive index. So does the bubble do the same by means of time dilation? Unlike a prism, the bubble has no sharp boundaries. Light entering at an angle should "curve" rather than diffract abruptly.
I expect light emanating/reflecting from the object to red-shift to a viewer outside the bubble, but this is not expected from light merely crossing the bubble's space. Will the visual effects resemble gravitational lensing by massive objects?