Symmetric Criticality and Magnetic Monopoles in General Relativity

Abstract

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.

Keywords

• Weyl method
• Palais principle of symmetric criticality
• solutions to Einstein’s equations
• magnetic monopole