How do you model curvature?

[EquisDeXD]

Space can bend in various ways, but its often depicted as some flat plane that then somehow extends to a higher 3rd dimension in the presence of gravity, but that doesn't make sense, a black hole isn't a dip in a plane, a black hole is a black hole from every infinitesimally possible side, but how do you model that in 3 dimensions? If you use some typical cubic graph, it seems like the units between increments of space get smaller as they approach the event horizon, but isn't the fabric of space becoming infinitely warped? Or how do you even measure real "degrees" of curvature? By what angle in degrees is Earth's gravity bending space at 500 miles from the surface? And what is it bent in the direction of?

Edited October 6, 2012 by EquisDeXD

[ajb]

I am not sure what you are asking here.

 

If you want to examine the causal structure of a black hole then Penrose diagrams are useful.