I am planning to apply to PhD courses at 2 different universities. Professor A is at the first school, and professor B is at the second school.
I already communicated with the professor A. I am also thinking of writing a contact e-mail to professor B.
Professor A and Professor B are quite close (academically), as they are working on the upcoming project as co-authors.
Would it be inappropriate if I contact professor B to show my academic interest?
I'm just worried that they might find it unethical to talk about my interest to them simultaneously.