Non-linear time theory is not inconsistent with any other physics, even within black holes. The reason for this is because non-linearity cannot be achieved except based on a series of steps which split distances over at least a c^4 series of steps within our time frame.
That being said, the last step need not occur even in black holes. What is required to go from linearity to non-linearity is a process which we may not completely understand because we do not experience it except at extremes of dimensional creation and destruction.
At present, our universe creates black holes (deep gravity wells) in different sizes which necessarily implies that they do not achieve non-linearity since weight would cease to exist at that point. The accumulation of gravity does involve dropping out of space which is an observed function on linear space and fusion occurs (as opposed to fission) in these high gravity environments and matter can be ejected and energy is ejected from these environments which can be (in the case of very high energy particles) a function of the movement from linearity to non-linearity. Something is happening here. The universe is clearly going non-linear. Why, however, does it not go completely non-linear where weight ceases to exist.
One idea would be that the universe only goes non-linear at the very beginning and very end. What effect if any this has expansion is more complicated to investigate. It doesn't matter that an artificial period of billion of years occurs in between these events since that is linearity which itself is artificial even though it matters to us and what leads to non-linearity is complex. However, this is the reason why determining if time goes non-linear is so important. It time goes non-linear and then comes back to being linear as a part of the expansion of space it would show that time can go non-linear in black holes.
So what's the purpose of all of this determination? Well, with all the scary shows on the end of the world I figure we have to come up with some way to get off this rock before the expiration date on the side. No, that sounds like a good reason, but there has to be some other reason...
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