In a static bounded universe, what happens to particles that hit the edge? Consider a flat universe. The metric tensor is 
$$g_{\mu\nu}=\left(\begin{array}{cccc}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)$$
but this is just the topology. Usually, universes with edges are not considered because they are apparently difficult to deal with, but suppose we tried to consider one. If this universe is not expanding (or not expanding very fast), what will happen to fast moving particles like photons that reach the edge?
 A: 
In a static bounded universe, what happens to particles that hit the edge?

I venture to say nobody knows for sure. But it's an interesting question, because we have no evidence whatsoever that our universe is infinite or some kind of hypersphere. See this answer to a related  subject. The story goes that in the old days, people could not conceive of a world that was curved. They could only conceive of a world with an edge. Nowadays we have cosmologists who cannot conceive of a world that is not curved, they cannot conceive of a world with an edge. 

Consider a flat universe. The metric tensor is $$g_{\mu\nu}=\left(\begin{array}{cccc}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)$$ 
  but this is just the topology. Usually, universes with edges are not considered because they are apparently difficult to deal with, but suppose we tried to consider one. If this universe is not expanding (or not expanding very fast), what will happen to fast moving particles like photons that reach the edge?

Obviously there's no definitive answers to this, merely opinions. And my opinion is based on what Einstein said about space. That it isn't nothing. It's something. Something that you can't see or feel, but nevertheless there's something there, something that can be stressed, something that can have a state which we call a field. Something through which waves propagate. Something which, as per the recent LIGO news, waves. 
For an analogy, think of the E=hf photon as a water wave, think of space as water, and think of the universe as a droplet of water. Send a wave towards the edge, and what happens? It doesn't go through the edge. It undergoes total internal reflection. It bounces back. That's what I think will happen to a photon at the edge of the universe. Of course, there's no evidence for this hall of mirrors universe. But who knows, one day there might be. Take a look at the Hubble Ultra Deep Field image. Pick a prominent galaxy, then look over to the right and down a bit. There's a galaxy that looks rather similar. Funny that. 
 
