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Symmetries of linearized gravity from adjoint operators

Journal article
Authors S. Aksteiner
Thomas Bäckdahl
Published in Journal of Mathematical Physics
Volume 60
Issue 8
Pages 589
ISSN 0022-2488
Publication year 2019
Published at Department of Mathematical Sciences
Pages 589
Language en
Keywords equations, perturbations, separation, Physics
Subject categories Mathematical physics


Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and, in particular, the Kerr spacetime. One of them is of differential order four and coincides with a result of Cohen and Kegeles. The other one is a new operator of differential order six. The corresponding operator identities are based on the Teukolsky equation and the Teukolsky-Starobinsky identities, respectively. The method applies to other field equations as well, which is illustrated with the Maxwell equation. The resulting symmetry operators are connected to Hertz and Debye potentials as well as to the separability of the Teukolsky equation for both Maxwell and linearized gravity.

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