Black holes and the time issue

[Tachyonie]

Good day to you all, I am total amateur so people with high physics degree don't need to waste their time since this question is very easy to answer I am sure...

Time gets slower and slower (atleast relative to us) as the gravitational field gets stronger and stronger right? (If I am wrong just skip the rest and call me an idiot)
I can see two logical problems with this postulate. The first one is the big bang. How could the universe expand in such a short time if at the beginning, there was so much energy/matter that the time dilation must have been huge if not infinite? Or was it really that slow but since we live inside the universe we can't tell the difference?
Second one is the black holes. If I am right, as a star collapse into itself it has bigger and bigger escape speed and the time dilation increases. How can this star ever reach it's terminal state of singularity if eventually time virtually stops and atleast from our perspective the star never collapses completely?

Thank you for your time!

 

[mathman]

The time dilation apples to utside observers. It does not apply to the frame of the black hole itself. Similarly at the big bang, it did not apply to the universe itself. The same holds for a collapsing star - within its own frame, there is no dilation.

 

[Tachyonie]

The time dilation apples to utside observers. It does not apply to the frame of the black hole itself. Similarly at the big bang, it did not apply to the universe itself. The same holds for a collapsing star - within its own frame, there is no dilation.

Yes indeed, I thought of it somehow like that but it's useful to have it confirmed from somebody else. However I didn't just mean that time stops for the collapsing star/black hole, but from our perspective it does. So in infinite future the star does collapse, but what point is there if universe might not exist anymore?
My poin was that there is no true singularity in black holes since eventually the time slows down so much that billions upon billions years can pass for the outter space and virtually no time for the black hole. Thus concluding that there is no true singularity in our space *yet*.