Is time going backwards beyond the event horizon of a black hole? For an outside observer the time seems to stop at the event horizon. My intuition suggests, that if it stops there, then it must go backwards inside. 
Is this the case?
This question is a followup for the comment I made for this question: Are we inside a black hole?

Food for thought: if time stops at the event horizon (for an outside observer), for inside, my intuition suggests, time should go backwards. So for matter, that's already inside when the black hole forms, it won't fall towards a singularity but would fall outwards towards the event horizon due to this time reversal. So inside there would be an outward gravitational force. It would be fascinating if it turns out that all this cosmological redshift, and expansion we observe, is just the effect of an enormous event horizon outside pulling the stuff outwards.

So from outside: we see nothing fall in, and see nothing come out.
And from inside: we see nothing fall out, and see nothing come in.
Hopefully the answers make this clear, and I learn a bit more about the GR. :)
 A: Your intuition is misguided, time does not run backwards inside a black hole. For an observer inside a black hole, time passes in a perfectly "normal" way, such as it does at the horizon. The stopping of time of time at the horizon is, as you mentioned, a phenomenon that only an outside observer experiences. It can for example be measured by noticing change of the received frequency of light signals which are emitted from near the horizon at constant frequency.
A: It's easy to forget that, in the context of relativity, there is no universal time.  You write:

For an outside observer the time seems to stop at the event horizon.
  My intuition suggests, that if it stops there, then it must go
  backwards inside. Is this the case?

But your intuition doesn't seem to take into account that, for an observer falling into the hole, time doesn't stop at the event horizon.
The point is that one must be much more careful in their thinking about time within the framework of general relativity where time is a coordinate and coordinates are arbitrary.
In fact, within the event horizon, the radial coordinate becomes time-like and the time coordinate becomes space-like.  This simply means that, to "back up" inside the event horizon is as impossible as moving backwards in time outside the event horizon.
In other words, the essential reason it is impossible to avoid the singularity once within the horizon is precisely that one must move forward through time which, due to the extreme curvature within the horizon, means moving towards the central singularity.
A: Let me make sure I have this right. An outside observer watching an object entering a black hole will either see that object slow down to the point where it seems to stop or the object will disappear because the light from that object can't escape the gravitational pull. 
As for an observer entering the black hole, time continues to go on as normal or/and the outside universe seems to age faster the deeper the observer enters the black hole; this I have a major problem with.
I agree with the general consensus about how an outside observer would perceive an object entering a black hole because we have conducted experiments that show time is affected by gravity; the differences in time on earth compared to space. What I don't agree with is how time is perceived by an observer entering a black hole because it is all a mystery. Maybe time does go backwards.
Maybe time continues as normal. Maybe the black hole is a giant worm hole to another dimension. I only bring this up because some of the responses to this question seem to indicate they know what happens as though it is fact. The truth is the black holes are a mystery.
The physics that we believe rule the known universe could be completely different than the physics that occur in a black hole. 
