This paper derives a new symmetry operator S that commutes with a normalized form of the wave ope... more This paper derives a new symmetry operator S that commutes with a normalized form of the wave operator in a Kerr background. Differently to previously known symmetry operators for the wave operator, S contains only a partial time derivative of the first order, but not of higher order. The key for the proof of commutation is an abstract lemma that might also be applicable to other separable wave equations. As a consequence, in formulations of the initial value problem for the wave equation in terms of first-order systems of PDE and related formulations, S leads on a operator that formally commutes with the infinitesimal generator of time evolution and therefore is a candidate for the generator of a strongly continuous semigroup or group of symmetries. Finally, a new conservation law is derived for the scalar field in the gravitational field of a Kerr black hole that is associated with a Killing tensor of that spacetime.
This paper derives a new symmetry operator S that commutes with a normalized form of the wave ope... more This paper derives a new symmetry operator S that commutes with a normalized form of the wave operator in a Kerr background. Differently to previously known symmetry operators for the wave operator, S contains only a partial time derivative of the first order, but not of higher order. The key for the proof of commutation is an abstract lemma that might also be applicable to other separable wave equations. As a consequence, in formulations of the initial value problem for the wave equation in terms of first-order systems of PDE and related formulations, S leads on a operator that formally commutes with the infinitesimal generator of time evolution and therefore is a candidate for the generator of a strongly continuous semigroup or group of symmetries. Finally, a new conservation law is derived for the scalar field in the gravitational field of a Kerr black hole that is associated with a Killing tensor of that spacetime.
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