On naked singularities and the collapse of self-gravitating Higgs fields

We consider the problem of collapse of a self-gravitating Higgs field, with potential bounded below by a (possibly negative) constant. The behaviour at infinity may be either asymptotically flat or asymptotically AdS. This problem has received much attention as a source for possible violations of weak cosmic censorship in string theory. In this paper, we prove under spherical symmetry that ``first singularities'' arising in the non-trapped region must necessarily emanate from the centre. In particular, this excludes the formation of a certain type of naked singularity which was recently conjectured to occur.