A conserved current for perturbations of Einstein-Maxwell space-times

Abstract

Using the fact that the Einstein-Maxwell field equations arise from a Lagrangian variational principle, a closed 3-form associated with solutions of the perturbation equations is constructed. By dualizing with respect to the metric compatible volume element, a covariantly conserved current-known as the symplectic current - is obtained. A useful formula for the component of this current normal to a non-null hypersurface is found by ‘pulling back’ the 3-form to this hypersurface. This formula is then used to evaluate the symplectic current for axisymmetric, polar perturbations with harmonic time dependence of axisymmetric, static space-times. It is shown that this current reproduces the current found by Chandrasekhar & Ferrari.