I am a final-year PhD student doing my research in the field of theoretical physics. Soon, I will start applying for postdoc positions in different universities, primarily related to my area of expertise, which is holographic chaos. The problem I am facing is that there are few postdoc opportunities for my specialization, so I worry that I need to switch to a related one.
Would it be a good idea to personally mail prospective professors even if the institute doesn't have open postdoc positions in my area of expertise?