  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.
