Solutions to gravity in 2+1 dimensions /by Michael John Duncan.

Our best theory of the gravitational force at large distance scales is general_x000D_relativity in 3+1 dimensions (3 spatial dimensions plus 1 time dimension). Our best_x000D_theory of small scale phenomena comes from quantum mechanics/quantum field_x000D_theory. These two theories are incompatible with one another in the sense that no_x000D_one has yet successfully given a quantum theory of gravity. Exploration into 2+1_x000D_dimensional gravity began as a means of looking for a quantum theory of gravity in_x000D_the simpler context of 2+1 dimensions. In 2+1 dimensions many of the objections_x000D_to quantizing gravity that occur in 3+1 dimensions are absent or not as severe. In_x000D_this thesis we investigated certain solutions to 2+1 dimensional gravity which were_x000D_motivated through the ??rubber sheet model?? of general relativity. One class of_x000D_solutions we found was of the form, ds2 = dt2 _ r2d_2 _ dr2 , with the restriction 1_krn_x000D__that 0 _ n _ 2. We also found a class of 2+1 dimensional gravity solutions of the form, ds2 = (1 _ krn)dt2 _ r2d_2 _ dr2 , with the same restriction that 0 _ n _ 2._x000D__1_krn_x000D_Some of these solutions represented interesting cosmological space-times in 2 + 1_x000D_dimensions