# Modeling an infinite delay system

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.

• Maybe as $y(t)=0$ ?
– MBaz
Jan 22, 2017 at 22:27
• @MBaz sorry the parameter is z not y. So, the parameter z has nothing to do with output. Yes, y(t) = 0. However, I want the system to have an infinite delay, but not zero output (I don't know if this a valid argument)
– hbak
Jan 22, 2017 at 22:33
• So what is the output for $t<\infty$?
– MBaz
Jan 23, 2017 at 3:25
• @MBaz based on my question it's zero.
– hbak
Jan 23, 2017 at 4:30
• $y(t)=x(t-5000)$ (where time is measured in years). Note that a factor $\text{exp}(j\phi)$ is equivalent to a time delay only for sine and cosine signals.
– MBaz
Jan 23, 2017 at 15:11