Separability of the Killing–Maxwell system underlying the generalized angular momentum constant in the Kerr–Newman black hole metrics Available to Purchase

The concept of a Killing–Maxwell system may be defined by the relation Â_[μ;v];ρ =(4π/3)ĵ_[μg_ν]. In such a system the one‐form Â_μ is interpretable as the four‐potential of an electromagnetic field F̂_μv, whose source current ĵ ^μ is an ordinary Killing vector. Such a system determines a canonically associated duality class of source‐free electromagnetic fields, its own dual being a Killing–Yano tensor, such as was found by Penrose [Ann. N.Y. Acad. Sci. 224, 125 (1973)] (with Floyd) to underlie the generalized angular momentum conservation law in the Kerr black hole metrics, the existence of the Killing–Yano tensor being also a sufficient condition for that of the Killing–Maxwell system. In the Kerr pure vacuum metric and more generally in the Kerr–Newman metrics for which a member of the associated family of source‐free fields is coupled in gravitationally, it is shown that the gauge of the Killing–Maxwell one‐form may be chosen so that it is expressible (in the standard Boyer–Lindquist coordinates) by 1/2 (a² cos ² θ−r²)dt+ 1/2 a(r²−a²)sin² θ dφ, the corresponding source current being just (4π/3)(∂/∂t). It is found that this one‐form (like that of the standard four‐potential for the associated source‐free field) satisfies the special requirement for separability of the corresponding coupled charged (scalar or Dirac spinor) wave equations.