I was trying to imagine what 3D objects would look like in 4D and I came across this question about visualizing the 4th dimension here: Visualizing the 4th dimension.

It was said that you could visualize 3D objects as projections/shadows of 4D objects. Almost all the questions I could see about this talk about 3D cubes being considered like an intersection of a Tesseract. This following question contains an answer with a nice visualization of the 3D intersections of a Tesseract as an animation: What would a tesseract actually look like?

Which lead me to thinking about what would a visualization of a black hole (in our 3D universe) look like as a 4D object? i.e. What kind of 4D object would have to exist to produce an intersection that would look like a black hole? In particular what would the singularity look like, also an infinitesimal point in 4D? I guess the event horizon could be considered as a (hollow?) sphere?