If black holes swallow everything and assumes that the black holes do not get out the things from them, then can we consider a black hole as an infinite delay system? It takes the input and it is a super slow system that has an infinite delay so they do not give an output?
If yes, How can model such a system? I thought about modeling the system like this:
y(x) = x + jz.
where x is the input and j is the imaginary part. z is a parameter within the system(black hole) itself.
the phase shift for such a system can be given by:
tan-1(z/x) and this quantity must approaches to infinity which is impossible since the maximum value for the function is pi/2. So how can we adjust the parameter z to give the infinite delay?
A side note: I gave the black hole as an example, so the question is mainly about how to model the infinite delay system.