How does Gauss's divergence law work in a closed finite universe? Let's say the universe were a 4-sphere, with a single electron. How can I work out the field of the electron? If I draw a 3-sphere around the electron, then I split space into two regions. One region contains an electron, so Gauss's law tells me that the flux through the sphere is -e*4pi. But the other region doesn't contain any electron, so Gauss's law tells me that the flux through the sphere going the other way is 0. That's inconsistent. It seems if I think about it a little more, it makes no sense to have an infinite range force in finite space. An electron's field lines would "wrap around" and overlap itself onto infinity.