How to politely inform potential PhD supervisor that I must wait before responding to an offer? (Two-body problem)

In my opinion, since you are already accepted, there is no harm in telling about the two-body problem; if you end up going to University B, [email protected] would likely feel better about that reason than some negative impression of them personally or of University A.

You are well within your rights to take the full 30 days to decide. Certainly not all professors are equally versed or sympathetic towards the two-body problem, but most have experienced it, if not personally, through their colleagues, friends, etc.

Ultimately I think it is your choice whether or not to explain your reasoning, but I would personally lose a bit of respect towards your [email protected] if they were unable to accept you stating simply "My offer gives me 30 days to respond, and I would like to take that entire time to ensure I make the right decision for me. I will inform you immediately of my decision once it is made."

I would encourage you to tell your potential advisor, the department, your partner's potential advisor, and their department, about your situation.

I was in a similar situation (in the US), and not only were the advisors and departments sympathetic, they were actively supportive. They helped introduce us to other potential advisors, sought additional funding, etc.

In my situation, we had spent multiple years applying to PhD programs to find a good fit for both of us. In the first year, we did not mention the two-body problem to anyone until after the decision deadline. When I mentioned the challenges we were facing, one professor expressed regret that I had not informed the department sooner. He explained that they try to help in such situations, as it is often beneficial to the university to compromise on joint hires.

The following year, we were more up front about our two-body situation. We experienced no negative reactions and a lot of support. It took us an additional year to find funding for both of us, but we are now both in the PhD program at the same university.

Many academics have experienced 2-body problems. It is becoming more common in the US for universities to joint hire, and it looks like this might be extending to the PhD level as well. I would welcome commenters who can assess whether this is also true internationally.