Separability of the Killing--Maxwell system underlying the generalized angular momentum constant in the Kerr--Newman black hole metrics

Journal Article · Wed Jul 01 00:00:00 EDT 1987 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527509· OSTI ID:6779719

Carter, B

The concept of a Killing--Maxwell system may be defined by the relation A-italic-circumflex/sub (//sub ..mu..//sub ;//sub v//sub );//sub rho/ = (4..pi../3)j-italic-circumflex/sub (//sub ..mu../g/sub ..nu..//sub )/. In such a system the one-form A-italic-circumflex/sub ..mu../ is interpretable as the four-potential of an electromagnetic field F-italic-circumflex/sub ..mu..//sub v/, whose source current j-italic-circumflex /sup ..mu../ 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 (a/sup 2/ cos /sup 2/ theta-r/sup 2/)dt+ 1/2 a(r/sup 2/-a/sup 2/)sin/sup 2/ theta dphi, the corresponding source current being just (4..pi../3)(partial/partialt). 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.

• Research Organization: Department d' Astrophysique Relativiste et Cosmologie, Centre National de la Recherche Scientifique, Observatoire de Paris, 92 Meudon, France
• OSTI ID: 6779719
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ANGULAR MOMENTUM
BLACK HOLES
CONSERVATION LAWS
DEGREES OF FREEDOM
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC FIELDS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATION
KERR METRIC
MAXWELL EQUATIONS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
SPINORS
TENSORS
WAVE EQUATIONS