Relativity in 2 spatial dimensions

[cam875]

do all of the equations and postulates of the general theory of relativity apply in a universe with only 2 spatial and one time instead of 3 spatial and one time.

 

[robphy]

One could try to play with "toy models" of GR with lower spacetime dimensionality.
However, the lower dimensionality severely reduces the number of independent components of the curvature tensor.

 

[cam875]

will if there is only 2 spatial dimensions than all the matter warping space will also be 2 dimensions so would the tensor be the same and all of the equations applying to 3d matter in 3d space be the same.

 

[JesseM]

Here's a pretty detailed discussion of the analogue of GR in a universe with 2 spatial dimensions:

http://gregegan.customer.netspace.net.au/SCIENCE/GR2plus1/GR2plus1.html

Basically, it seems you can't actually have spacetime curvature at any finite distance from a massive object in 2D, although you can have point particles which have the property that when you travel around them the angle is less than 360, like traveling around the tip of a cone (which is also a surface that's flat everywhere in differential geometry terms, since you can 'unroll' it into a flat surface with a pie-shaped wedge cut out, see http://www.allendesigns.com/AreaofCone/AreaofCone.htm ). There's a somewhat less technical discussion here:

http://www.theory.caltech.edu/people/patricia/ttif.html

(see especially the section on 'What is the spacetime geometry?')