I'm standing on a black hole, is light approaching red or blue?

[Mordred]

That ambiguity is one reason that I am glad none of my cosmology textbooks (12) of them nor any recent thesis papers I've read (lost count on the number). Utilize the bound/unbound terminology anymore. They simply state finite or infinite is unknown then discuss the 3 geometries and describe their effects on light paths.

 

[WannabeNewton]

That ambiguity is one reason that I am glad none of my cosmology textbooks (12) of them nor any recent thesis papers I've read (lost count on the number). Utilize the bound/unbound terminology anymore. They simply state finite or infinite is unknown then discuss the 3 geometries and describe their effects on light paths.

12 books wow! Quite the cosmology connoisseur I see ! And yes I agree that simply stating the 3 geometries should be enough since the local geometrical properties (but not global topological properties such as your torus example) follow suit from simply prescribing these 3 geometries. One book that I think discusses the terminology and "technicalities" in a nice way is the book George Jones recently recommended to me: "Gravitation: Foundations and Frontiers" - T.Padmanabhan

 

[PeterDonis]

I don't understand your talking about finite but bounded.

Oops, I meant to say "finite but unbounded". You're quite right, finite but bounded doesn't make sense. I have fixed my previous post.

 

[PeterDonis]

it may very well be that Peter was referring to how $S^{3}$ is bounded in the second sense mentioned above.

I was referring to $S^3$ being a manifold without boundary in the topological sense; but as phinds pointed out, I should have said "unbounded", not "bounded" (I have now corrected that in my previous post). I don't know if there's a more precise term that has that specific meaning without the ambiguities you mention. One more reason to be wary of expressing things in natural language instead of in math.

 

[phinds]

Oops, I meant to say "finite but unbounded". You're quite right, finite but bounded doesn't make sense. I have fixed my previous post.

I had to laugh at myself. After chiding you about this, I happened to notice that my own post #23 used bounded where I MEANT to say UNbounded (I've gone back now and edited it)

 

[Mordred]

Thanks for the reference WannabeNewton. I'll have to add that to my collection.