Global Monopole metric in 2+1-dimensions

Abstract

In order to obtain the geometry of a global monopole without cosmological constant and electric charge in $2+1-$ dimensions we make use of the broken $% O(2)$ symmetry. In the absence of exact solution we determine the series solutions for both the metric and monopole functions in a consistent manner that satisfy all equations in appropriate powers. The new expansion elements are of the form $\frac{1}{r^{n}}\left( \ln r\right) ^{m},$ for the radial distance $r$ and positive integers $m$ and $n$ constrained by $m\leq n$. To the lowest order of expansion we find that in analogy with the negative cosmological constant the geometry of the global monopole acts repulsively, i.e., in the absence of a cosmological constant the global monopole plays at large distances the role of a negative cosmological constant.