I'm going to get a phd student in trouble for not paying cover at a bar
Why do you want to get him into trouble?
The student has been making a lot of trouble in the bar.
If a person is continually causing issues on top of not paying their cover, it should be brought up with bar management. Talking to management shouldn't mess up their phd studies!
I have to teach him a lesson for being rude and for having a bad influence on the other students.
Well it is good that you want to let people know that he is refusing to pay his cover. However, it may be better to just go right to the head of the bar instead.