# Separability of Maxwell equation in rotating black hole spacetime and its geometric aspects

## TL;DR

This paper explores the geometric origins of symmetry operators that enable the separation of Maxwell's equations in rotating black hole spacetimes, advancing understanding of their mathematical structure.

## Contribution

It introduces a method to derive symmetry operators from the geometric properties linked to hidden symmetries of the Kerr-NUT-(A)dS spacetime.

## Key findings

- Symmetry operators can be constructed from geometric quantities.
- The formalism simplifies Maxwell's equations in complex spacetimes.
- The approach enhances understanding of separability in black hole backgrounds.

## Abstract

Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by separation of variables. In this formalism the differential operators that commute with the operators of the equations of motion, called symmetry operators, played a key role to establish the separable structure. In this work we propose a method to reproduce these commuting symmetry operators in terms of the geometric quantities associated to the hidden symmetry of the background spacetime.