A conserved energy for axially symmetric Newman–Penrose–Maxwell scalars on Kerr black holes

Abstract

We show that there exists a 1-parameter family of positive-definite and conserved energy functionals for axially symmetric Newman–Penrose–Maxwell scalars on the maximal space-like hypersurfaces in the exterior of Kerr black holes. It is also shown that the Poisson bracket within this 1-parameter family of energies vanishes on the maximal hypersurfaces.