In order to obtain the geometry of a global monopole without cosmological constant and electric charge in 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 for the radial distance and positive integers and constrained by . 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.

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