I‘ve found plenty of articles explaining this and understand that it has to do with voltage differences at sharp corners of the object, but could find no direct research sources. Does someone know a paper that goes into the geometry of metal objects in microwave ovens and why it‘s fine to put a metallic spoon into a cup of water to be heated in the microwave?
it has to do with voltage differences at sharp corners of the object,
It's not voltage differences. It's electrical field strength. When the electric field strength exceeds the breakdown value for air, you'll get a spark. And the field strength tends to "concentrate" at sharp corners of electrodes.
But these are general principles that apply in lots of places other than utensils in microwave ovens. For example, this also applies to making a lightning rod, or a spark plug.
Just like after we found that objects have the same acceleration due to gravity regardless of mass people didn't write different papers about how potatoes of different mass fall at the same rate, and hay bales of different mass fall at the same rate; pointy electrodes in any electrostatic scenario are where the sparks form and there's no real need for a special paper about how pointy parts of utensils in microwaves produce sparks.