Basically, you are allowed to enter Germany for the purpose of studying, which also includes a doctorate. Furthermore, citizens of EU countries do not need a so-called "valid reason for entry". Third-country nationals usually have to prove that they have a place at a university (find out more about visa requirements here). It is important that the studies cannot be completed entirely from abroad. However, since most universities offer a mixture of online and face-to-face studies or you have to be on site at least for certain exams, proof of compulsory attendance is usually not required. Please check with your (host) university in case of doubt. In addition, for all entries by air, a negative test result not older than 48 hours must be presented. Instead of a test result, proof of complete vaccination with a vaccine accredited in the EU or proof of recovery can also be presented. Furthermore, there are special entry requirements for different regions of residence, which vary from region to region: