I already wrote this somewhere else. If the curvature of space around a gravity source is proportional to the square root of distance, like the gravitational time dilation formula, then negative distance (internal space) becomes a complex number and gets an extra dimension - the real number and the imaginary. Is there any truth to that?
A few concerns.
The biggest is that you are using the simplification as the basis for your theory.
There are many ways to think about what happens around the borders of a black hole. While it is popular to think of it as a curvature of space/time, that is a simplification that makes it easier to explain to a lay-person. You've got a big heavy elastic surface, you put something big and heavy on it and a dent or bend is visible, the concept is communicated.
While the concept works readily enough for an ELI5-style world, it gets into some complicated PhD-style mathematics and theories. There is the equivalence principle that comes into play between gravity and mass, the relative dilation of both time and space, and a bunch of other stuff that it interesting but ultimately makes my eyes glaze over when Peter (my blackhole-studying brother) starts discussing it all. The curvature of space isn't really a curvature of all -- not in the spatial sense -- but a compression/dilation based on the interplay between gravity and mass at extreme values.
The stretchy surface of space/time simplification is not physically accurate, it is just an easy way to explain it.
As for complex or imaginary numbers adding a spatial dimension, note that numeric dimensionality does not equate to spatial dimensionality. You can add all kinds of non-spatial dimensions to the world around you. I've seen people try to add many other items as dimensions, such as colors and time. While they may serve as orthogonal dimensions for a specific purpose (e.g. the color of a thing is independent of the location of the thing) they are not additional spatial dimensions (Up/down, left/right, forward/back, and new dimension). All attempts to throw in a fourth spatial dimension break nearly all observable conditions and constants. Among the most easy of these would be the tunneling and slowing of motion; light moving along a fourth spatial dimension would appear to change speed in the three we can measure, but the magnitude of the speed of light measured in three dimensions is an apparent constant. Light moving completely along that fourth dimension would appear to be suspended in location, stopped or nearly stopped in the three dimensions we see resulting in a variable 3D speed of light, yet for all observations light moves at a constant speed in 3D.
A fourth spatial dimension would break most of the fundamental physical constants, like the speed of light, Planck's constant and the quanta of distances, magnetic and electric constants, and the rest. Is it possible that inside a black hole, somewhere we cannot currently directly observe, there are such radically different fundamental physics? Sure, why not. But it is an extremely long leap to make that inside a region of high mass like a black hole there would be a change to the fundamentals of physics.
If you want to imagine up a situation where inside a black hole you have a fourth spatial dimension, either (more likely) you will be on track for a creative science fiction novel, or (far less likely) you will be on the track for a PhD thesis in theoretical physics. If you have the mathematical chops to revise all the fundamental physics rules so they basically work with a fourth spatial dimension, then go for it. But I doubt that is the case.