Like Germany, Spain in a signatory of the Schengen Agreement. In order to enter Germany and Spain it is thus sufficient to apply for one Schengen visa if it is not possible for the professor to travel to the Schengen area without a visa.
The question as to which of several places of residence is considered the principal place of residence is only relevant under German law if a resident maintains several residences within Germany. Residences abroad are not taken into consideration. If a person with a residence abroad maintains only one residence in Germany, this residence is considered his or her only and thus principle domestic residence.
In your case, you will maintain one German residence for the duration of your stay abroad, which means you do not need to end or transfer your registration or have your identity card changed. The case would be different if you were to give up your domestic residence for the duration of your research stay. In this case you would have to notify the authorities of your departure and your identity card would be marked with: "Kein Wohnsitz im Inland" (No domestic residence).
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Last updated: 24 April 2023