To be honest this is well covered in wikipedia and Tim did really well on that section

Godel Metric

Key points I would highlight for you

- It isn't a viable model for the universe but it is an exact solution to Einsteins equations, so this universe in theory could exist

- It highlights the problem of observers disagreeing and finding a good reference frame in the model is challenging.

- If you follow Hawking's logic the model shows you what a rotating universe would look like and we can rule out our universe is rotating.

I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.