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.

中文翻译：

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克尔时空线性化重力的一类守恒流

我们为克尔背景上的线性重力构建了一类守恒电流。我们的程序受 Carter (1977) 发现的标量场电流的启发，是通过取对称算子定义的线性化爱因斯坦方程的解的辛积给出的。我们考虑与 Teukolsky 方程中变量分离相关的对称算子，以及由于爱因斯坦方程的自伴随性质而产生的对称算子。在几何光学极限中，与这些电流相关的电荷减少到其卡特常数正幂的引力子上的总和，很像标量场的守恒电流。我们进一步计算这些守恒电流通过零无穷大和视界的通量，并确定哪些是有限的。