Gravitacional field of a global defect

Global topological defects described by real scalar field in (3,1) dimensions coupled to gravity are analyzed. We consider a class of scalar potentials with explicit dependence with distance, evading Derrick's theorem and leading to defects with spherical symmetry. The analysis shows that the defects have finite energy on flat space, contrary to the observed for the global monopole. With the aim to study the gravitational field produced by such defects, after an {\it Ansatz} for the static metric with spherical symmetry, we obtain the coupled system of Einstein and field equations. On the Newtonian approximation, we numerically find that the defects have a repulsive gravitational field. This field is like one generated by a negative mass distributed on a spherical shell. In the weak gravity regime a relation between the Newtonian potential and one of the metric coefficients is obtained. The numerical analysis in this regime leads to a spacetime with a deficit solid angle on the core of the defect.