A class of conserved currents for linearized gravity in the Kerr spacetime. (29th December 2020)

• Record Type: Journal Article
• Authors: Grant, Alexander M; Flanagan, Éanna É
• Is Part Of: Classical and quantum gravity. Volume 38:Number 5(2021)
• Publication Date: 2020-12-29
• Subjects: Kerr perturbation theory -- Carter constant -- conserved currents; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/abc3f7
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: We construct a class of conserved currents for linearized gravity on a Kerr background. Our procedure, motivated by the current for scalar fields discovered by Carter (1977), is given by taking the symplectic product of solutions to the linearized Einstein equations that are defined by symmetry operators. We consider symmetry operators that are associated with separation of variables in the Teukolsky equation, as well as those arising due the self-adjoint nature of the Einstein equations. In the geometric optics limit, the charges associated with these currents reduce to sums over gravitons of positive powers of their Carter constants, much like the conserved current for scalar fields. We furthermore compute the fluxes of these conserved currents through null infinity and the horizon and identify which are finite.