Symmetric Criticality and Magnetic Monopoles in General Relativity

The Weyl method for finding solutions in general relativity using symmetry by varying an action with respect to a reduced set of field variables is known to fail in some cases. We add to the list of failures by considering an application of the Weyl method to a magnetically charged spherically symmetric source, obtaining an incorrect geometry. This is surprising, because the same method, applied to electrically charged central bodies correctly produces the Reissner-Nordström spacetime.

Singularity-free interaction in dilaton-Maxwell electrodynamics

An effective potential is created for the dynamics of a test particle, which preserves dilatation symmetry for nonlinear static dilaton-Maxwell background. It is found that the central interaction in this theory is singularity-free everywhere; it vanishes at short distances and demonstrates Coulomb behavior far from the source. It is shown that static and spherically symmetric source behaves like a soliton: it has the finite energy characteristics that are inversely proportional to the dilaton-Maxwell coupling constant.