Consider the 3 dimensional projective space minus the infinity point, and empty of matter.
We see that it has ADM mass. In other words, a perfectly fine geometry, orientable and asymptomatically flat, that has an unusual topology in our thought experiment, gives rise to mass in the absence of matter.
The question is why we don't consider the emergence of a sort of mass without matter a contradiction or a problem in the theory of general relativity, and instead accept the possibility of such a universe?
I'd like to see both physical and mathematical arguments if possible.
Please watch this lecture video for further details: