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 an exact solution, we determine the series solutions for both the metric and monopole functions in a consistent manner that satisfies all equations in appropriate powers. The new expansion elements are of the form 1/r(n)(In r)(m), for the radial distance r and positive integers m and n constrained by m <= 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.