Does time exist at the center of a Black Hole? A black hole is a wormhole resulting from a dead Star which is capable of sucking any mass/matter  along its path due to Gravity. I was wondering what time would be like at the central point of the wormhole, would it exist at all or would it be faster or slower?
 A: In standard GR, nothing exists at the center of a black hole. The center of a black hole is a singularity, and because GR fails at that point it is simply removed from the manifold. That means that the singularity is not part of spacetime. 
To answer your question more realistically, we believe that GR is an approximate theory that fails well before you reach the center. Unfortunately, we have no good alternative theory with which to answer the question in the region where GR fails. We simply don’t have any data from that regime and it is very hard to formulate a good theory without data. So there very well could be time at the center, but we simply don’t have a good way to even guess. 
A: First off, I'm not an expert, but I think I can help you a bit with this question.
yes and no in a way. Time always exists for an observer. if you were a singular point and would observe your own time, it would (by very definition) run consistently. But, and this is a big but, entropy is maximal at the surface of a black hole. So nothing will happen, only Hawking radiation, which in turn will shrink de surface of the black hole. So from if you were to follow information through time at its point in space, it will enter a black hole and then be turned into radiation (practically) instantly and radiate away. there is no moment at which it is timeless, yet for an outside observer, the dissipation of the information can take time. 
But that is the tricky bit, time is defined in terms of events. So if nothing happens for nobody, no time passes and there would be no way to observe it. So if you would think about it, time can never really stop since this would totally disconnect the timeless place in space from the rest of space. Because how long would it be timeless? That is impossible to ask since the timeless part would not be able to keep the time of how long it would be timeless. 
Sidenote: 
Blackholes are not wormholes. Wormholes are the concept of connecting 2 places in the universe via spacetime. But This requires spacetime to be curved, but so far, all observations have not yet dismissed that the universe isn't curved. (which indicates that we should seriously consider the possibility of a flat universe). 
Blackholes are just places in spacetime in which pathways of particles/information converge. 
A: Our observation of black holes (and all observations of all observers outside the black hole) are stopping at its event horizon, and it is not possible to go beyond. According to the No-Hair theorem, the characteristics of black holes are very limited, they have a mass, an electric charge and an angular momentum. From this point of view, it does not make sense to search the time of the "center of the black hole". 
We can only speculate what is going on inside of the black hole. The calculation of the path of an "infalling observer" according to the Schwarzschild metric seems to show that from the point of view of an infalling observer, nothing special is happening, time is running normally. In contrast, for outside observers, the infalling observer is eternally approaching the event horizon without ever crossing it. From these elements we could deduce that the time inside a black hole (and inside all black holes) would be happening after the end of our time, because the infalling observer can only cross the event horizon when our time is no more existent.
But such calculation is pure speculation, with view to the fact that according to general relativity, all observation ends at the event horizon. We are not sure that the Schwarzschild metric is applying also inside the event horizeon. For outside observers, a black hole is one solidary element, and there is no proper time inside the black hole, but there is only the observed coordinate time according to our spacetime coordinates.
