General relativity in 1+1 spacetime dimensions

[jdstokes]

Has anyone ever analysed Einstein's equations in 1+1 spactime dimensions?

It seems to me like this would provide a convenient toy model for teaching or learning general relativity. For one thing the spacetime curvature can be visualized as curvature of a 2-dimensional surface.

 

[tiny-tim]

Hi jdstokes!

But how could you give the students any idea about orbits?

Hardly anything moves in a straight line under gravity.

 

[coalquay404]

Has anyone ever analysed Einstein's equations in 1+1 spactime dimensions?

It seems to me like this would provide a convenient toy model for teaching or learning general relativity. For one thing the spacetime curvature can be visualized as curvature of a 2-dimensional surface.

Two dimensional manifolds are conformally flat, so there's very little useful information to be gleaned from a 1+1 dimensional model of GR. (There are many other reasons why 1+1 GR is trivial, including the fact that as you reduce the number of spatial dimensions your model will no longer give you the correct Newtonian limit, but this is the most immediately apparent one.)

The lowest-dimensional non-trivial case is (2+1)-dimensional gravity. This case has essentially been solved completely, at least in the classical sense. Carlip has a very readable review of it on Living Reviews:

http://relativity.livingreviews.org/Articles/lrr-2005-1/index.html [Broken]