Every year, I receive many inquiries regarding graduate studies. Most of these inquiries make it clear that the writer does not know how the admissions system works. So let me explain.
I do not make decisions regarding graduate student admission. As is the case in most and probably all North American universities, there is no such thing here as a PhD position offered by a supervisor or group. Positions in the programme are offered by the Faculty of Graduate Studies and Research, and held within the Department. The decision on acceptance is made by the department's Associate Chair for Graduate Studies, on the advice of the Graduate Admissions Committee. That committee invites a few faculty members to comment on each application. Every year I am asked to comment on a few applications relevant to my area. That is my only role in the process.
If you'd like to be a graduate student here, you must apply to the Department. See https://www.ualberta.ca/mathematical-and-statistical-sciences/graduate-studies
My department, the Department of Mathematical and Statistical Sciences, hosts several programmes including the PhD programme in Mathematical Physics. Most theoretical physics, including most relativity, is in the Department of Physics. That department has a separate application procedure. See https://www.ualberta.ca/physics/graduate-studies
If you are accepted into a thesis-based programme, my department will also offer a package of financial support. Typically, this involves a Teaching Assistantship position and/or scholarship support, and an anticipated eventual contribution from the grant of your research supervisor.
Usually the research supervisor is chosen after you arrive and have taken some courses. (Prior to your arrival, the department will appoint an advisor for you, who helps you choose your courses and settle in to the programme. Advisors sometimes become supervisors, but not always.) However, if you have a particular supervisor or research area in mind, it is wise to contact that person in advance to see if he or she will be interested in having students. (They may be considering retirement, or may have too many students, or may not have a sufficient research grant to support students.) It is also wise to list such people on your application, even if you haven't contacted them. This helps the admissions committee to choose the most suitable faculty members to comment on your application.Feel free to contact me, especially if you are seriously interested in my area, but please don't send me your file and expect me to review it. There is a formal procedure for that. And a positive response from me means only that, if you are accepted, then after you arrive and are doing well in your courses, if you are still interested in my area, we can talk about potential research projects. You can take it for granted that I am interested in having students, in principle.