I am a theoretical computer science PhD student. My childhood friend (my present roommate) is in the 3rd year of his pure mathematics PhD program. Very recently we both worked on a problem on combinatorial geometry and got some interesting results to publish. However both of our dissertation topics are way different from this work, so we don't want to involve our advisors in this matter. This was kind of our joint fun project. We don't know whether it's academically unethical to publish paper(s) as PhD students without including our advisor(s).
(Note: We have nothing to lose even if they reject our paper right away, but we don't want the editor of the journal to mail the chair about this matter. Maybe I'm thinking too much because I've never done this kind of thing before.)