A monopole formed as a consequence of the spontaneous breakdown of a global symmetry should have a mass that grows linearly with the distance off its core. It was recently shown by Barriola and Vilenkin that the gravitational effect of this configuration is equivalent to that of a deficit solid angle in the metric, plus that of a relatively tiny mass at the origin. Here we show that this small effective mass is negative. Global monopoles thus share with other topological defects, such as domain walls and global strings, a repulsive gravitational potential. We solve numerically the coupled equations for the metric and the scalar field, to precisely determine this repulsive potential and in order to analyze the solution when gravitational effects are already significant close to the monopole core. We study the motion of test particles in a monopole background, and discuss the possible implications of a negative effective mass.

• Received 20 March 1990

DOI:https://doi.org/10.1103/PhysRevD.42.2626