I'm thinking about the time dilation in terms of distance from the singularity, to the event horizon and outside it.
After a black hole has lost its necessary mass to maintain its singularity through hawking radiation, and explodes, it should shoot matter outwards far enough to spread out and away from the original position relative to the singularity. Is the rate at which the time dilation of space and how it will return to "outside event horizon" levels going to be linear based upon the radius from the singularity? as in the speed of light radially inwards? Would it be some non-linear function where the outer edge of the event horizon returned to normal curvature at an exponential rate towards the center?
My inclination is that the space outside the event horizon would behave differently than internal space upon exploding, atleast in terms of how drastically the curvature and time-dilation are changing.