A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes

TL;DR

This paper introduces a family of positive, conserved energy functionals for axially symmetric Maxwell scalars on Kerr black holes, revealing their mathematical properties and potential for analyzing electromagnetic fields in curved spacetime.

Contribution

It constructs a novel 1-parameter family of conserved energies for Maxwell scalars in Kerr spacetime, with a detailed analysis of their properties.

Findings

Existence of a positive-definite, conserved energy family

Vanishing Poisson bracket within the energy family

Applicability to axially symmetric Maxwell fields 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 spacelike 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.